Find general formula for the termsDeriving a formula to find the sum of a series.Find general formula for a seriesHow to find the general formula for this recursive problem?Demonstration of a simple formulaFinding general formula for sequenceGeneral formula for harmonic sequenceHow can I tell if the sequence re-cycles?The general term of such a recursion formulaFind an explicit formula for the recursive formulaThe general nth derivative formula of $(1-x/4)^-2$
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Find general formula for the terms
Deriving a formula to find the sum of a series.Find general formula for a seriesHow to find the general formula for this recursive problem?Demonstration of a simple formulaFinding general formula for sequenceGeneral formula for harmonic sequenceHow can I tell if the sequence re-cycles?The general term of such a recursion formulaFind an explicit formula for the recursive formulaThe general nth derivative formula of $(1-x/4)^-2$
$begingroup$
Find a general formula for the terms of the sequence
$$a_n=left frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649,dots right$$
I don't know how to approach this question as it is not arithmetic or geometric. I know the denominator is geometric increasing by a factor of $7$ but I can't find what the numerator should be for the general formula for the terms. Anyone know what it is?
sequences-and-series
edited Apr 22 at 14:09
MarianD
2,3461619
asked Apr 21 at 16:56
RaV1oLLiRaV1oLLi
292
New contributor
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Find a general formula for the terms of the sequence
$$a_n=left frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649,dots right$$
I don't know how to approach this question as it is not arithmetic or geometric. I know the denominator is geometric increasing by a factor of $7$ but I can't find what the numerator should be for the general formula for the terms. Anyone know what it is?
sequences-and-series
edited Apr 22 at 14:09
MarianD
2,3461619
asked Apr 21 at 16:56
RaV1oLLiRaV1oLLi
292
New contributor
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
1
$begingroup$
Where does it come from?
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:14
$begingroup$
My online calculus questions platform called Mobius(used to be Maple TA). I believe it must be a mistake as nothing I input is giving me the correct answer.
$endgroup$
– RaV1oLLi
Apr 21 at 17:16
$begingroup$
Have you put it into OEIS?
$endgroup$
– Dave
Apr 21 at 17:22
$begingroup$
This is in the OEIS, but not much else - oeis.org/A081657
$endgroup$
– Peter Foreman
Apr 21 at 17:23
1
$begingroup$
Nobody can tell you the correct answer. Whatever answer you give, the proposer can tell you that you are wrong. You an't win this kind of game.
$endgroup$
– Somos
Apr 21 at 18:55
add a comment |
$begingroup$
Find a general formula for the terms of the sequence
$$a_n=left frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649,dots right$$
I don't know how to approach this question as it is not arithmetic or geometric. I know the denominator is geometric increasing by a factor of $7$ but I can't find what the numerator should be for the general formula for the terms. Anyone know what it is?
sequences-and-series
edited Apr 22 at 14:09
MarianD
2,3461619
asked Apr 21 at 16:56
RaV1oLLiRaV1oLLi
292
New contributor
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Find a general formula for the terms of the sequence
$$a_n=left frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649,dots right$$
I don't know how to approach this question as it is not arithmetic or geometric. I know the denominator is geometric increasing by a factor of $7$ but I can't find what the numerator should be for the general formula for the terms. Anyone know what it is?
sequences-and-series
sequences-and-series
edited Apr 22 at 14:09
MarianD
2,3461619
asked Apr 21 at 16:56
RaV1oLLiRaV1oLLi
292
New contributor
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 22 at 14:09
MarianD
2,3461619
asked Apr 21 at 16:56
RaV1oLLiRaV1oLLi
292
New contributor
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 22 at 14:09
MarianD
2,3461619
edited Apr 22 at 14:09
MarianD
2,3461619
edited Apr 22 at 14:09
MarianD
2,3461619
2,3461619
asked Apr 21 at 16:56
RaV1oLLiRaV1oLLi
292
New contributor
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 21 at 16:56
RaV1oLLiRaV1oLLi
292
asked Apr 21 at 16:56
RaV1oLLiRaV1oLLi
292
292
New contributor
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
RaV1oLLi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
$begingroup$
Where does it come from?
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:14
$begingroup$
My online calculus questions platform called Mobius(used to be Maple TA). I believe it must be a mistake as nothing I input is giving me the correct answer.
$endgroup$
– RaV1oLLi
Apr 21 at 17:16
$begingroup$
Have you put it into OEIS?
$endgroup$
– Dave
Apr 21 at 17:22
$begingroup$
This is in the OEIS, but not much else - oeis.org/A081657
$endgroup$
– Peter Foreman
Apr 21 at 17:23
1
$begingroup$
Nobody can tell you the correct answer. Whatever answer you give, the proposer can tell you that you are wrong. You an't win this kind of game.
$endgroup$
– Somos
Apr 21 at 18:55
add a comment |
1
$begingroup$
Where does it come from?
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:14
$begingroup$
My online calculus questions platform called Mobius(used to be Maple TA). I believe it must be a mistake as nothing I input is giving me the correct answer.
$endgroup$
– RaV1oLLi
Apr 21 at 17:16
$begingroup$
Have you put it into OEIS?
$endgroup$
– Dave
Apr 21 at 17:22
$begingroup$
This is in the OEIS, but not much else - oeis.org/A081657
$endgroup$
– Peter Foreman
Apr 21 at 17:23
1
$begingroup$
Nobody can tell you the correct answer. Whatever answer you give, the proposer can tell you that you are wrong. You an't win this kind of game.
$endgroup$
– Somos
Apr 21 at 18:55
1
1
$begingroup$
Where does it come from?
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:14
$begingroup$
Where does it come from?
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:14
$begingroup$
My online calculus questions platform called Mobius(used to be Maple TA). I believe it must be a mistake as nothing I input is giving me the correct answer.
$endgroup$
– RaV1oLLi
Apr 21 at 17:16
$begingroup$
My online calculus questions platform called Mobius(used to be Maple TA). I believe it must be a mistake as nothing I input is giving me the correct answer.
$endgroup$
– RaV1oLLi
Apr 21 at 17:16
$begingroup$
Have you put it into OEIS?
$endgroup$
– Dave
Apr 21 at 17:22
$begingroup$
Have you put it into OEIS?
$endgroup$
– Dave
Apr 21 at 17:22
$begingroup$
This is in the OEIS, but not much else - oeis.org/A081657
$endgroup$
– Peter Foreman
Apr 21 at 17:23
$begingroup$
This is in the OEIS, but not much else - oeis.org/A081657
$endgroup$
– Peter Foreman
Apr 21 at 17:23
1
1
$begingroup$
Nobody can tell you the correct answer. Whatever answer you give, the proposer can tell you that you are wrong. You an't win this kind of game.
$endgroup$
– Somos
Apr 21 at 18:55
$begingroup$
Nobody can tell you the correct answer. Whatever answer you give, the proposer can tell you that you are wrong. You an't win this kind of game.
$endgroup$
– Somos
Apr 21 at 18:55
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
The general formula for an (infinite) sequence of (e. g. real) numbers from the finite number $n$ of its (first) members is in principle impossible, as the next (not listed) $(n+1)^mathrmth$ member may be an arbitrary number, and there is still a formula for expressing $a_1, dots, a_n, a_n+1,$ e. g. as a polynomial of order $n$:
$$a_k = sum_i=0^nb_ik^i,quad k = 1, dots,n+1$$
The process for finding coefficients $b_0, dots, b_n$ is straightforward enough.
In other words, if someone will find the formula for your "sequence", there is still the infinity number of other formulas, giving different sequences, but all of them producing your "sequence", i. e. $$frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649.$$
Note:
It means that all psychological tests of type
What is the next number of the sequence $1, 2, 3, 4, 5?$
are in principle meaningless ones, because you may tell "$1762$", and then show to surprised psychologist a formula supporting the correctness of your answer:
$$a_k = 439over30k^5-439over 2k^4+7463over 6k^3-6585over 2k^2+60158over 15k-1756$$
If he/she will not trust you, launch SageMath, which will produce accurate, non-rounded results, and write commands
sage: var("k")
sage: a(k) = (439/30)*k^5 - (439/2)*k^4+(7463/6)*k^3-(6585/2)*k^2+(60158/15)*k-1756
sage: a(1), a(2), a(3), a(4), a(5), a(6), a(7), a(8)
to obtain the result
(1, 2, 3, 4, 5, 1762, 10543, 36884)
(and to give the psychologist two more members for free).
Note 2:
It doesn't mean that there is not a simpler formula - including a recurrent one or other "recipe" - for the same (finite) sequence.
For example, there is so simple one for the rather not so trivial sequence
$$colorblue1, 11, 21, 1211, 111221$$
that even 6-7 year-old child is able to write down the next element ($colorred312211$) if you tell it the rule, or - perhaps - even without telling it.
No, you have no chance to discover this simple rule (supposing your age is $10$+). Don't waste your time. It's a good advice, believe me.
(Googling for it is a much better approach.)
answered Apr 21 at 17:34
MarianDMarianD
2,3461619
$endgroup$
add a comment |
$begingroup$
The general term seems to be
$$a_n=frac2(7^n)+(-3)^n7^n=2+left(-frac37right)^n$$
But the last term is given by
$$a_6=2-left(frac37right)^6$$
so this formula does not always work. A suitable formula could be
$$a_n=begincases2-left(frac37right)^n&nequiv0mod6\
2+left(-frac37right)^n &textotherwise
endcases$$
answered Apr 21 at 17:13
Peter ForemanPeter Foreman
8,7701321
$endgroup$
add a comment |
$begingroup$
The numerator of the $n$-th term seems to be
$$2cdot 7^n+(-1)^n 3^n. $$
answered Apr 21 at 17:05
BernardBernard
125k743119
$endgroup$
$begingroup$
May I ask how you got to this answer? Or is trial and error the only method?Edit: I inputted this answer into the online question and it came out as incorrect.
$endgroup$
– RaV1oLLi
Apr 21 at 17:07
$begingroup$
I was thinking the same, but what about the last term? $234569ne 2(7^6)+3^6$
$endgroup$
– Peter Foreman
Apr 21 at 17:07
1
$begingroup$
@PeterForeman Arg, yes, the last is $2(7)^6colorred-3^6$!
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:10
1
$begingroup$
@RaV1oLLi: I noticed the numerators are the successive powers of $7$, and the numerators were not far from twice the denominator, with a corrective term. So I subtracted twice the denominators from the numerators, and tried to see a pattern. I tested only the 5 first terms.
$endgroup$
– Bernard
Apr 21 at 17:20
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The general formula for an (infinite) sequence of (e. g. real) numbers from the finite number $n$ of its (first) members is in principle impossible, as the next (not listed) $(n+1)^mathrmth$ member may be an arbitrary number, and there is still a formula for expressing $a_1, dots, a_n, a_n+1,$ e. g. as a polynomial of order $n$:
$$a_k = sum_i=0^nb_ik^i,quad k = 1, dots,n+1$$
The process for finding coefficients $b_0, dots, b_n$ is straightforward enough.
In other words, if someone will find the formula for your "sequence", there is still the infinity number of other formulas, giving different sequences, but all of them producing your "sequence", i. e. $$frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649.$$
Note:
It means that all psychological tests of type
What is the next number of the sequence $1, 2, 3, 4, 5?$
are in principle meaningless ones, because you may tell "$1762$", and then show to surprised psychologist a formula supporting the correctness of your answer:
$$a_k = 439over30k^5-439over 2k^4+7463over 6k^3-6585over 2k^2+60158over 15k-1756$$
If he/she will not trust you, launch SageMath, which will produce accurate, non-rounded results, and write commands
sage: var("k")
sage: a(k) = (439/30)*k^5 - (439/2)*k^4+(7463/6)*k^3-(6585/2)*k^2+(60158/15)*k-1756
sage: a(1), a(2), a(3), a(4), a(5), a(6), a(7), a(8)
to obtain the result
(1, 2, 3, 4, 5, 1762, 10543, 36884)
(and to give the psychologist two more members for free).
Note 2:
It doesn't mean that there is not a simpler formula - including a recurrent one or other "recipe" - for the same (finite) sequence.
For example, there is so simple one for the rather not so trivial sequence
$$colorblue1, 11, 21, 1211, 111221$$
that even 6-7 year-old child is able to write down the next element ($colorred312211$) if you tell it the rule, or - perhaps - even without telling it.
No, you have no chance to discover this simple rule (supposing your age is $10$+). Don't waste your time. It's a good advice, believe me.
(Googling for it is a much better approach.)
answered Apr 21 at 17:34
MarianDMarianD
2,3461619
$endgroup$
add a comment |
$begingroup$
The general formula for an (infinite) sequence of (e. g. real) numbers from the finite number $n$ of its (first) members is in principle impossible, as the next (not listed) $(n+1)^mathrmth$ member may be an arbitrary number, and there is still a formula for expressing $a_1, dots, a_n, a_n+1,$ e. g. as a polynomial of order $n$:
$$a_k = sum_i=0^nb_ik^i,quad k = 1, dots,n+1$$
The process for finding coefficients $b_0, dots, b_n$ is straightforward enough.
In other words, if someone will find the formula for your "sequence", there is still the infinity number of other formulas, giving different sequences, but all of them producing your "sequence", i. e. $$frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649.$$
Note:
It means that all psychological tests of type
What is the next number of the sequence $1, 2, 3, 4, 5?$
are in principle meaningless ones, because you may tell "$1762$", and then show to surprised psychologist a formula supporting the correctness of your answer:
$$a_k = 439over30k^5-439over 2k^4+7463over 6k^3-6585over 2k^2+60158over 15k-1756$$
If he/she will not trust you, launch SageMath, which will produce accurate, non-rounded results, and write commands
sage: var("k")
sage: a(k) = (439/30)*k^5 - (439/2)*k^4+(7463/6)*k^3-(6585/2)*k^2+(60158/15)*k-1756
sage: a(1), a(2), a(3), a(4), a(5), a(6), a(7), a(8)
to obtain the result
(1, 2, 3, 4, 5, 1762, 10543, 36884)
(and to give the psychologist two more members for free).
Note 2:
It doesn't mean that there is not a simpler formula - including a recurrent one or other "recipe" - for the same (finite) sequence.
For example, there is so simple one for the rather not so trivial sequence
$$colorblue1, 11, 21, 1211, 111221$$
that even 6-7 year-old child is able to write down the next element ($colorred312211$) if you tell it the rule, or - perhaps - even without telling it.
No, you have no chance to discover this simple rule (supposing your age is $10$+). Don't waste your time. It's a good advice, believe me.
(Googling for it is a much better approach.)
answered Apr 21 at 17:34
MarianDMarianD
2,3461619
$endgroup$
add a comment |
$begingroup$
The general formula for an (infinite) sequence of (e. g. real) numbers from the finite number $n$ of its (first) members is in principle impossible, as the next (not listed) $(n+1)^mathrmth$ member may be an arbitrary number, and there is still a formula for expressing $a_1, dots, a_n, a_n+1,$ e. g. as a polynomial of order $n$:
$$a_k = sum_i=0^nb_ik^i,quad k = 1, dots,n+1$$
The process for finding coefficients $b_0, dots, b_n$ is straightforward enough.
In other words, if someone will find the formula for your "sequence", there is still the infinity number of other formulas, giving different sequences, but all of them producing your "sequence", i. e. $$frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649.$$
Note:
It means that all psychological tests of type
What is the next number of the sequence $1, 2, 3, 4, 5?$
are in principle meaningless ones, because you may tell "$1762$", and then show to surprised psychologist a formula supporting the correctness of your answer:
$$a_k = 439over30k^5-439over 2k^4+7463over 6k^3-6585over 2k^2+60158over 15k-1756$$
If he/she will not trust you, launch SageMath, which will produce accurate, non-rounded results, and write commands
sage: var("k")
sage: a(k) = (439/30)*k^5 - (439/2)*k^4+(7463/6)*k^3-(6585/2)*k^2+(60158/15)*k-1756
sage: a(1), a(2), a(3), a(4), a(5), a(6), a(7), a(8)
to obtain the result
(1, 2, 3, 4, 5, 1762, 10543, 36884)
(and to give the psychologist two more members for free).
Note 2:
It doesn't mean that there is not a simpler formula - including a recurrent one or other "recipe" - for the same (finite) sequence.
For example, there is so simple one for the rather not so trivial sequence
$$colorblue1, 11, 21, 1211, 111221$$
that even 6-7 year-old child is able to write down the next element ($colorred312211$) if you tell it the rule, or - perhaps - even without telling it.
No, you have no chance to discover this simple rule (supposing your age is $10$+). Don't waste your time. It's a good advice, believe me.
(Googling for it is a much better approach.)
answered Apr 21 at 17:34
MarianDMarianD
2,3461619
$endgroup$
The general formula for an (infinite) sequence of (e. g. real) numbers from the finite number $n$ of its (first) members is in principle impossible, as the next (not listed) $(n+1)^mathrmth$ member may be an arbitrary number, and there is still a formula for expressing $a_1, dots, a_n, a_n+1,$ e. g. as a polynomial of order $n$:
$$a_k = sum_i=0^nb_ik^i,quad k = 1, dots,n+1$$
The process for finding coefficients $b_0, dots, b_n$ is straightforward enough.
In other words, if someone will find the formula for your "sequence", there is still the infinity number of other formulas, giving different sequences, but all of them producing your "sequence", i. e. $$frac117,frac10749,frac659343,frac48832401,frac3337116807,frac234569117649.$$
Note:
It means that all psychological tests of type
What is the next number of the sequence $1, 2, 3, 4, 5?$
are in principle meaningless ones, because you may tell "$1762$", and then show to surprised psychologist a formula supporting the correctness of your answer:
$$a_k = 439over30k^5-439over 2k^4+7463over 6k^3-6585over 2k^2+60158over 15k-1756$$
If he/she will not trust you, launch SageMath, which will produce accurate, non-rounded results, and write commands
sage: var("k")
sage: a(k) = (439/30)*k^5 - (439/2)*k^4+(7463/6)*k^3-(6585/2)*k^2+(60158/15)*k-1756
sage: a(1), a(2), a(3), a(4), a(5), a(6), a(7), a(8)
to obtain the result
(1, 2, 3, 4, 5, 1762, 10543, 36884)
(and to give the psychologist two more members for free).
Note 2:
It doesn't mean that there is not a simpler formula - including a recurrent one or other "recipe" - for the same (finite) sequence.
For example, there is so simple one for the rather not so trivial sequence
$$colorblue1, 11, 21, 1211, 111221$$
that even 6-7 year-old child is able to write down the next element ($colorred312211$) if you tell it the rule, or - perhaps - even without telling it.
No, you have no chance to discover this simple rule (supposing your age is $10$+). Don't waste your time. It's a good advice, believe me.
(Googling for it is a much better approach.)
answered Apr 21 at 17:34
MarianDMarianD
2,3461619
edited Apr 22 at 3:08
answered Apr 21 at 17:34
MarianDMarianD
2,3461619
answered Apr 21 at 17:34
MarianDMarianD
2,3461619
answered Apr 21 at 17:34
MarianDMarianD
2,3461619
2,3461619
add a comment |
add a comment |
$begingroup$
The general term seems to be
$$a_n=frac2(7^n)+(-3)^n7^n=2+left(-frac37right)^n$$
But the last term is given by
$$a_6=2-left(frac37right)^6$$
so this formula does not always work. A suitable formula could be
$$a_n=begincases2-left(frac37right)^n&nequiv0mod6\
2+left(-frac37right)^n &textotherwise
endcases$$
answered Apr 21 at 17:13
Peter ForemanPeter Foreman
8,7701321
$endgroup$
add a comment |
$begingroup$
The general term seems to be
$$a_n=frac2(7^n)+(-3)^n7^n=2+left(-frac37right)^n$$
But the last term is given by
$$a_6=2-left(frac37right)^6$$
so this formula does not always work. A suitable formula could be
$$a_n=begincases2-left(frac37right)^n&nequiv0mod6\
2+left(-frac37right)^n &textotherwise
endcases$$
answered Apr 21 at 17:13
Peter ForemanPeter Foreman
8,7701321
$endgroup$
add a comment |
$begingroup$
The general term seems to be
$$a_n=frac2(7^n)+(-3)^n7^n=2+left(-frac37right)^n$$
But the last term is given by
$$a_6=2-left(frac37right)^6$$
so this formula does not always work. A suitable formula could be
$$a_n=begincases2-left(frac37right)^n&nequiv0mod6\
2+left(-frac37right)^n &textotherwise
endcases$$
answered Apr 21 at 17:13
Peter ForemanPeter Foreman
8,7701321
$endgroup$
The general term seems to be
$$a_n=frac2(7^n)+(-3)^n7^n=2+left(-frac37right)^n$$
But the last term is given by
$$a_6=2-left(frac37right)^6$$
so this formula does not always work. A suitable formula could be
$$a_n=begincases2-left(frac37right)^n&nequiv0mod6\
2+left(-frac37right)^n &textotherwise
endcases$$
answered Apr 21 at 17:13
Peter ForemanPeter Foreman
8,7701321
edited Apr 21 at 17:18
answered Apr 21 at 17:13
Peter ForemanPeter Foreman
8,7701321
answered Apr 21 at 17:13
Peter ForemanPeter Foreman
8,7701321
answered Apr 21 at 17:13
Peter ForemanPeter Foreman
8,7701321
8,7701321
add a comment |
add a comment |
$begingroup$
The numerator of the $n$-th term seems to be
$$2cdot 7^n+(-1)^n 3^n. $$
answered Apr 21 at 17:05
BernardBernard
125k743119
$endgroup$
$begingroup$
May I ask how you got to this answer? Or is trial and error the only method?Edit: I inputted this answer into the online question and it came out as incorrect.
$endgroup$
– RaV1oLLi
Apr 21 at 17:07
$begingroup$
I was thinking the same, but what about the last term? $234569ne 2(7^6)+3^6$
$endgroup$
– Peter Foreman
Apr 21 at 17:07
1
$begingroup$
@PeterForeman Arg, yes, the last is $2(7)^6colorred-3^6$!
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:10
1
$begingroup$
@RaV1oLLi: I noticed the numerators are the successive powers of $7$, and the numerators were not far from twice the denominator, with a corrective term. So I subtracted twice the denominators from the numerators, and tried to see a pattern. I tested only the 5 first terms.
$endgroup$
– Bernard
Apr 21 at 17:20
add a comment |
$begingroup$
The numerator of the $n$-th term seems to be
$$2cdot 7^n+(-1)^n 3^n. $$
answered Apr 21 at 17:05
BernardBernard
125k743119
$endgroup$
$begingroup$
May I ask how you got to this answer? Or is trial and error the only method?Edit: I inputted this answer into the online question and it came out as incorrect.
$endgroup$
– RaV1oLLi
Apr 21 at 17:07
$begingroup$
I was thinking the same, but what about the last term? $234569ne 2(7^6)+3^6$
$endgroup$
– Peter Foreman
Apr 21 at 17:07
1
$begingroup$
@PeterForeman Arg, yes, the last is $2(7)^6colorred-3^6$!
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:10
1
$begingroup$
@RaV1oLLi: I noticed the numerators are the successive powers of $7$, and the numerators were not far from twice the denominator, with a corrective term. So I subtracted twice the denominators from the numerators, and tried to see a pattern. I tested only the 5 first terms.
$endgroup$
– Bernard
Apr 21 at 17:20
add a comment |
$begingroup$
The numerator of the $n$-th term seems to be
$$2cdot 7^n+(-1)^n 3^n. $$
answered Apr 21 at 17:05
BernardBernard
125k743119
$endgroup$
The numerator of the $n$-th term seems to be
$$2cdot 7^n+(-1)^n 3^n. $$
answered Apr 21 at 17:05
BernardBernard
125k743119
answered Apr 21 at 17:05
BernardBernard
125k743119
answered Apr 21 at 17:05
BernardBernard
125k743119
answered Apr 21 at 17:05
BernardBernard
125k743119
125k743119
$begingroup$
May I ask how you got to this answer? Or is trial and error the only method?Edit: I inputted this answer into the online question and it came out as incorrect.
$endgroup$
– RaV1oLLi
Apr 21 at 17:07
$begingroup$
I was thinking the same, but what about the last term? $234569ne 2(7^6)+3^6$
$endgroup$
– Peter Foreman
Apr 21 at 17:07
1
$begingroup$
@PeterForeman Arg, yes, the last is $2(7)^6colorred-3^6$!
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:10
1
$begingroup$
@RaV1oLLi: I noticed the numerators are the successive powers of $7$, and the numerators were not far from twice the denominator, with a corrective term. So I subtracted twice the denominators from the numerators, and tried to see a pattern. I tested only the 5 first terms.
$endgroup$
– Bernard
Apr 21 at 17:20
add a comment |
$begingroup$
May I ask how you got to this answer? Or is trial and error the only method?Edit: I inputted this answer into the online question and it came out as incorrect.
$endgroup$
– RaV1oLLi
Apr 21 at 17:07
$begingroup$
I was thinking the same, but what about the last term? $234569ne 2(7^6)+3^6$
$endgroup$
– Peter Foreman
Apr 21 at 17:07
1
$begingroup$
@PeterForeman Arg, yes, the last is $2(7)^6colorred-3^6$!
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:10
1
$begingroup$
@RaV1oLLi: I noticed the numerators are the successive powers of $7$, and the numerators were not far from twice the denominator, with a corrective term. So I subtracted twice the denominators from the numerators, and tried to see a pattern. I tested only the 5 first terms.
$endgroup$
– Bernard
Apr 21 at 17:20
$begingroup$
May I ask how you got to this answer? Or is trial and error the only method?Edit: I inputted this answer into the online question and it came out as incorrect.
$endgroup$
– RaV1oLLi
Apr 21 at 17:07
$begingroup$
May I ask how you got to this answer? Or is trial and error the only method?Edit: I inputted this answer into the online question and it came out as incorrect.
$endgroup$
– RaV1oLLi
Apr 21 at 17:07
$begingroup$
I was thinking the same, but what about the last term? $234569ne 2(7^6)+3^6$
$endgroup$
– Peter Foreman
Apr 21 at 17:07
$begingroup$
I was thinking the same, but what about the last term? $234569ne 2(7^6)+3^6$
$endgroup$
– Peter Foreman
Apr 21 at 17:07
1
1
$begingroup$
@PeterForeman Arg, yes, the last is $2(7)^6colorred-3^6$!
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:10
$begingroup$
@PeterForeman Arg, yes, the last is $2(7)^6colorred-3^6$!
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:10
1
1
$begingroup$
@RaV1oLLi: I noticed the numerators are the successive powers of $7$, and the numerators were not far from twice the denominator, with a corrective term. So I subtracted twice the denominators from the numerators, and tried to see a pattern. I tested only the 5 first terms.
$endgroup$
– Bernard
Apr 21 at 17:20
$begingroup$
@RaV1oLLi: I noticed the numerators are the successive powers of $7$, and the numerators were not far from twice the denominator, with a corrective term. So I subtracted twice the denominators from the numerators, and tried to see a pattern. I tested only the 5 first terms.
$endgroup$
– Bernard
Apr 21 at 17:20
add a comment |
RaV1oLLi is a new contributor. Be nice, and check out our Code of Conduct.
RaV1oLLi is a new contributor. Be nice, and check out our Code of Conduct.
RaV1oLLi is a new contributor. Be nice, and check out our Code of Conduct.
RaV1oLLi is a new contributor. Be nice, and check out our Code of Conduct.
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Where does it come from?
$endgroup$
– Jean-Claude Arbaut
Apr 21 at 17:14
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My online calculus questions platform called Mobius(used to be Maple TA). I believe it must be a mistake as nothing I input is giving me the correct answer.
$endgroup$
– RaV1oLLi
Apr 21 at 17:16
$begingroup$
Have you put it into OEIS?
$endgroup$
– Dave
Apr 21 at 17:22
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This is in the OEIS, but not much else - oeis.org/A081657
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– Peter Foreman
Apr 21 at 17:23
1
$begingroup$
Nobody can tell you the correct answer. Whatever answer you give, the proposer can tell you that you are wrong. You an't win this kind of game.
$endgroup$
– Somos
Apr 21 at 18:55