What’s the sum of this series? [on hold]How to prove $sum_n=0^infty fracn^22^n = 6$?How can I find a closed form for this partial sum. $sum_n=1^kfracn^33^n$How to sum this series for $pi/2$ directly?What is the closed form sum of this series?What is the sum of the following infinite seriesComputing the sum of an infinite seriesSum of Reciprocals of the Fibonacci SeriesFind the sum of this infinite seriesSum of this infinite series…What is the sum of this telescoping series?Sum the infinite series:help with sum of infinite series, stuck in problem
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What’s the sum of this series? [on hold]
How to prove $sum_n=0^infty fracn^22^n = 6$?How can I find a closed form for this partial sum. $sum_n=1^kfracn^33^n$How to sum this series for $pi/2$ directly?What is the closed form sum of this series?What is the sum of the following infinite seriesComputing the sum of an infinite seriesSum of Reciprocals of the Fibonacci SeriesFind the sum of this infinite seriesSum of this infinite series…What is the sum of this telescoping series?Sum the infinite series:help with sum of infinite series, stuck in problem
$begingroup$
What is the some of the infinite series?
$$
A(n)= fracn^33^n
$$
sequences-and-series limits
New contributor
$endgroup$
put on hold as off-topic by mfl, Kavi Rama Murthy, Jyrki Lahtonen, mrtaurho, Hans Lundmark Mar 11 at 6:54
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mfl, Kavi Rama Murthy, Jyrki Lahtonen, mrtaurho
add a comment |
$begingroup$
What is the some of the infinite series?
$$
A(n)= fracn^33^n
$$
sequences-and-series limits
New contributor
$endgroup$
put on hold as off-topic by mfl, Kavi Rama Murthy, Jyrki Lahtonen, mrtaurho, Hans Lundmark Mar 11 at 6:54
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mfl, Kavi Rama Murthy, Jyrki Lahtonen, mrtaurho
2
$begingroup$
Not sure I have the right to do homework for others. If you want help then please write what did you try.
$endgroup$
– Mark
Mar 10 at 21:27
1
$begingroup$
A few comments: 1. What are you studying, and what do you already know how to do? Adding none of this information leaves your question prone to downvoting or closevoting. 2. Did my edits accurately convey your intent? 3. In English, "series" is both singular and plural.
$endgroup$
– Brian Tung
Mar 10 at 21:27
$begingroup$
Hint: Have a look at en.wikipedia.org/wiki/Eulerian_number#Identities
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– Donald Splutterwit
Mar 10 at 21:30
$begingroup$
Possible duplicate of How to prove $sum_n=0^infty fracn^22^n = 6$?
$endgroup$
– Hans Lundmark
Mar 11 at 6:54
$begingroup$
See also math.stackexchange.com/questions/1969933/…
$endgroup$
– Hans Lundmark
Mar 11 at 6:55
add a comment |
$begingroup$
What is the some of the infinite series?
$$
A(n)= fracn^33^n
$$
sequences-and-series limits
New contributor
$endgroup$
What is the some of the infinite series?
$$
A(n)= fracn^33^n
$$
sequences-and-series limits
sequences-and-series limits
New contributor
New contributor
edited Mar 10 at 21:26
Brian Tung
26.3k32555
26.3k32555
New contributor
asked Mar 10 at 21:25
Michael romano barmakMichael romano barmak
22
22
New contributor
New contributor
put on hold as off-topic by mfl, Kavi Rama Murthy, Jyrki Lahtonen, mrtaurho, Hans Lundmark Mar 11 at 6:54
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mfl, Kavi Rama Murthy, Jyrki Lahtonen, mrtaurho
put on hold as off-topic by mfl, Kavi Rama Murthy, Jyrki Lahtonen, mrtaurho, Hans Lundmark Mar 11 at 6:54
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – mfl, Kavi Rama Murthy, Jyrki Lahtonen, mrtaurho
2
$begingroup$
Not sure I have the right to do homework for others. If you want help then please write what did you try.
$endgroup$
– Mark
Mar 10 at 21:27
1
$begingroup$
A few comments: 1. What are you studying, and what do you already know how to do? Adding none of this information leaves your question prone to downvoting or closevoting. 2. Did my edits accurately convey your intent? 3. In English, "series" is both singular and plural.
$endgroup$
– Brian Tung
Mar 10 at 21:27
$begingroup$
Hint: Have a look at en.wikipedia.org/wiki/Eulerian_number#Identities
$endgroup$
– Donald Splutterwit
Mar 10 at 21:30
$begingroup$
Possible duplicate of How to prove $sum_n=0^infty fracn^22^n = 6$?
$endgroup$
– Hans Lundmark
Mar 11 at 6:54
$begingroup$
See also math.stackexchange.com/questions/1969933/…
$endgroup$
– Hans Lundmark
Mar 11 at 6:55
add a comment |
2
$begingroup$
Not sure I have the right to do homework for others. If you want help then please write what did you try.
$endgroup$
– Mark
Mar 10 at 21:27
1
$begingroup$
A few comments: 1. What are you studying, and what do you already know how to do? Adding none of this information leaves your question prone to downvoting or closevoting. 2. Did my edits accurately convey your intent? 3. In English, "series" is both singular and plural.
$endgroup$
– Brian Tung
Mar 10 at 21:27
$begingroup$
Hint: Have a look at en.wikipedia.org/wiki/Eulerian_number#Identities
$endgroup$
– Donald Splutterwit
Mar 10 at 21:30
$begingroup$
Possible duplicate of How to prove $sum_n=0^infty fracn^22^n = 6$?
$endgroup$
– Hans Lundmark
Mar 11 at 6:54
$begingroup$
See also math.stackexchange.com/questions/1969933/…
$endgroup$
– Hans Lundmark
Mar 11 at 6:55
2
2
$begingroup$
Not sure I have the right to do homework for others. If you want help then please write what did you try.
$endgroup$
– Mark
Mar 10 at 21:27
$begingroup$
Not sure I have the right to do homework for others. If you want help then please write what did you try.
$endgroup$
– Mark
Mar 10 at 21:27
1
1
$begingroup$
A few comments: 1. What are you studying, and what do you already know how to do? Adding none of this information leaves your question prone to downvoting or closevoting. 2. Did my edits accurately convey your intent? 3. In English, "series" is both singular and plural.
$endgroup$
– Brian Tung
Mar 10 at 21:27
$begingroup$
A few comments: 1. What are you studying, and what do you already know how to do? Adding none of this information leaves your question prone to downvoting or closevoting. 2. Did my edits accurately convey your intent? 3. In English, "series" is both singular and plural.
$endgroup$
– Brian Tung
Mar 10 at 21:27
$begingroup$
Hint: Have a look at en.wikipedia.org/wiki/Eulerian_number#Identities
$endgroup$
– Donald Splutterwit
Mar 10 at 21:30
$begingroup$
Hint: Have a look at en.wikipedia.org/wiki/Eulerian_number#Identities
$endgroup$
– Donald Splutterwit
Mar 10 at 21:30
$begingroup$
Possible duplicate of How to prove $sum_n=0^infty fracn^22^n = 6$?
$endgroup$
– Hans Lundmark
Mar 11 at 6:54
$begingroup$
Possible duplicate of How to prove $sum_n=0^infty fracn^22^n = 6$?
$endgroup$
– Hans Lundmark
Mar 11 at 6:54
$begingroup$
See also math.stackexchange.com/questions/1969933/…
$endgroup$
– Hans Lundmark
Mar 11 at 6:55
$begingroup$
See also math.stackexchange.com/questions/1969933/…
$endgroup$
– Hans Lundmark
Mar 11 at 6:55
add a comment |
1 Answer
1
active
oldest
votes
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If $|x|<1$, $sum_n=1^infty x^n=fracx1-x$. Applying $left(xfracddxright)^3$ obtains $sum_n=1^infty n^3x^n$. Now set $x=frac13$.
$endgroup$
$begingroup$
(+1) Although, I do not like the notation $(xfracddx)^3$ to imply taking the derivative and multiplying by $x$ thrice.
$endgroup$
– Peter Foreman
Mar 10 at 21:35
$begingroup$
Is "thrice" a thing? I never heard that before. And what does $(xfracddx)^3$ mean?
$endgroup$
– Pink Panther
Mar 10 at 21:38
1
$begingroup$
@PinkPanther It means three times - in this case, the operator $xfracddx$.
$endgroup$
– J.G.
Mar 10 at 21:41
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If $|x|<1$, $sum_n=1^infty x^n=fracx1-x$. Applying $left(xfracddxright)^3$ obtains $sum_n=1^infty n^3x^n$. Now set $x=frac13$.
$endgroup$
$begingroup$
(+1) Although, I do not like the notation $(xfracddx)^3$ to imply taking the derivative and multiplying by $x$ thrice.
$endgroup$
– Peter Foreman
Mar 10 at 21:35
$begingroup$
Is "thrice" a thing? I never heard that before. And what does $(xfracddx)^3$ mean?
$endgroup$
– Pink Panther
Mar 10 at 21:38
1
$begingroup$
@PinkPanther It means three times - in this case, the operator $xfracddx$.
$endgroup$
– J.G.
Mar 10 at 21:41
add a comment |
$begingroup$
If $|x|<1$, $sum_n=1^infty x^n=fracx1-x$. Applying $left(xfracddxright)^3$ obtains $sum_n=1^infty n^3x^n$. Now set $x=frac13$.
$endgroup$
$begingroup$
(+1) Although, I do not like the notation $(xfracddx)^3$ to imply taking the derivative and multiplying by $x$ thrice.
$endgroup$
– Peter Foreman
Mar 10 at 21:35
$begingroup$
Is "thrice" a thing? I never heard that before. And what does $(xfracddx)^3$ mean?
$endgroup$
– Pink Panther
Mar 10 at 21:38
1
$begingroup$
@PinkPanther It means three times - in this case, the operator $xfracddx$.
$endgroup$
– J.G.
Mar 10 at 21:41
add a comment |
$begingroup$
If $|x|<1$, $sum_n=1^infty x^n=fracx1-x$. Applying $left(xfracddxright)^3$ obtains $sum_n=1^infty n^3x^n$. Now set $x=frac13$.
$endgroup$
If $|x|<1$, $sum_n=1^infty x^n=fracx1-x$. Applying $left(xfracddxright)^3$ obtains $sum_n=1^infty n^3x^n$. Now set $x=frac13$.
answered Mar 10 at 21:31
J.G.J.G.
29.8k22947
29.8k22947
$begingroup$
(+1) Although, I do not like the notation $(xfracddx)^3$ to imply taking the derivative and multiplying by $x$ thrice.
$endgroup$
– Peter Foreman
Mar 10 at 21:35
$begingroup$
Is "thrice" a thing? I never heard that before. And what does $(xfracddx)^3$ mean?
$endgroup$
– Pink Panther
Mar 10 at 21:38
1
$begingroup$
@PinkPanther It means three times - in this case, the operator $xfracddx$.
$endgroup$
– J.G.
Mar 10 at 21:41
add a comment |
$begingroup$
(+1) Although, I do not like the notation $(xfracddx)^3$ to imply taking the derivative and multiplying by $x$ thrice.
$endgroup$
– Peter Foreman
Mar 10 at 21:35
$begingroup$
Is "thrice" a thing? I never heard that before. And what does $(xfracddx)^3$ mean?
$endgroup$
– Pink Panther
Mar 10 at 21:38
1
$begingroup$
@PinkPanther It means three times - in this case, the operator $xfracddx$.
$endgroup$
– J.G.
Mar 10 at 21:41
$begingroup$
(+1) Although, I do not like the notation $(xfracddx)^3$ to imply taking the derivative and multiplying by $x$ thrice.
$endgroup$
– Peter Foreman
Mar 10 at 21:35
$begingroup$
(+1) Although, I do not like the notation $(xfracddx)^3$ to imply taking the derivative and multiplying by $x$ thrice.
$endgroup$
– Peter Foreman
Mar 10 at 21:35
$begingroup$
Is "thrice" a thing? I never heard that before. And what does $(xfracddx)^3$ mean?
$endgroup$
– Pink Panther
Mar 10 at 21:38
$begingroup$
Is "thrice" a thing? I never heard that before. And what does $(xfracddx)^3$ mean?
$endgroup$
– Pink Panther
Mar 10 at 21:38
1
1
$begingroup$
@PinkPanther It means three times - in this case, the operator $xfracddx$.
$endgroup$
– J.G.
Mar 10 at 21:41
$begingroup$
@PinkPanther It means three times - in this case, the operator $xfracddx$.
$endgroup$
– J.G.
Mar 10 at 21:41
add a comment |
2
$begingroup$
Not sure I have the right to do homework for others. If you want help then please write what did you try.
$endgroup$
– Mark
Mar 10 at 21:27
1
$begingroup$
A few comments: 1. What are you studying, and what do you already know how to do? Adding none of this information leaves your question prone to downvoting or closevoting. 2. Did my edits accurately convey your intent? 3. In English, "series" is both singular and plural.
$endgroup$
– Brian Tung
Mar 10 at 21:27
$begingroup$
Hint: Have a look at en.wikipedia.org/wiki/Eulerian_number#Identities
$endgroup$
– Donald Splutterwit
Mar 10 at 21:30
$begingroup$
Possible duplicate of How to prove $sum_n=0^infty fracn^22^n = 6$?
$endgroup$
– Hans Lundmark
Mar 11 at 6:54
$begingroup$
See also math.stackexchange.com/questions/1969933/…
$endgroup$
– Hans Lundmark
Mar 11 at 6:55