Dtjytyk

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What’s the sum of this series? [on hold]

How to prove $sum_{n=0}^{infty} frac{n^2}{2^n} = 6$?How can I find a closed form for this partial sum. $sum_{n=1}^{k}frac{n^3}{3^n}$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

-3

$begingroup$

What is the some of the infinite series?

$$
A(n)= frac{n^3}{3^n}
$$

sequences-and-series limits

share|cite|improve this question

edited Mar 10 at 21:26

Brian Tung

26.2k32555

asked Mar 10 at 21:25

Michael romano barmakMichael romano barmak

22

New contributor

Michael romano barmak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

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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

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  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
  

  
  
  
  


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  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
  

  
  
  
  


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  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 $sum_{n=0}^{infty} frac{n^2}{2^n} = 6$?
  $endgroup$
  – 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 | 

-3

$begingroup$

What is the some of the infinite series?

$$
A(n)= frac{n^3}{3^n}
$$

sequences-and-series limits

share|cite|improve this question

edited Mar 10 at 21:26

Brian Tung

26.2k32555

asked Mar 10 at 21:25

Michael romano barmakMichael romano barmak

22

New contributor

Michael romano barmak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

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

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  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 $sum_{n=0}^{infty} frac{n^2}{2^n} = 6$?
  $endgroup$
  – 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?

$$
A(n)= frac{n^3}{3^n}
$$

sequences-and-series limits

share|cite|improve this question

edited Mar 10 at 21:26

Brian Tung

26.2k32555

asked Mar 10 at 21:25

Michael romano barmakMichael romano barmak

22

New contributor

Michael romano barmak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Mar 10 at 21:26

Brian Tung

26.2k32555

asked Mar 10 at 21:25

Michael romano barmakMichael romano barmak

22

New contributor

Michael romano barmak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Mar 10 at 21:26

Brian Tung

26.2k32555

asked Mar 10 at 21:25

Michael romano barmakMichael romano barmak

22

New contributor

Michael romano barmak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited Mar 10 at 21:26

Brian Tung

26.2k32555

edited Mar 10 at 21:26

Brian Tung

26.2k32555

asked Mar 10 at 21:25

Michael romano barmakMichael romano barmak

22

New contributor

Michael romano barmak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 10 at 21:25

Michael romano barmakMichael romano barmak

22

1 Answer
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If $|x|<1$, $sum_{n=1}^infty x^n=frac{x}{1-x}$. Applying $left(xfrac{d}{dx}right)^3$ obtains $sum_{n=1}^infty n^3x^n$. Now set $x=frac{1}{3}$.

share|cite|improve this answer

answered Mar 10 at 21:31

J.G.J.G.

30.1k23048

$endgroup$

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  $begingroup$
  (+1) Although, I do not like the notation $(xfrac{d}{dx})^3$ to imply taking the derivative and multiplying by $x$ thrice.
  $endgroup$
  – Peter Foreman
  Mar 10 at 21:35
  

  
  
  
  


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  $begingroup$
  Is "thrice" a thing? I never heard that before. And what does $(xfrac{d}{dx})^3$ mean?
  $endgroup$
  – Pink Panther
  Mar 10 at 21:38
  

  
  
  
  


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  1
  

  
  
  
  
  
  

  
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  @PinkPanther It means three times - in this case, the operator $xfrac{d}{dx}$.
  $endgroup$
  – J.G.
  Mar 10 at 21:41
  

  
  
  
  

add a comment | 

2

$begingroup$

If $|x|<1$, $sum_{n=1}^infty x^n=frac{x}{1-x}$. Applying $left(xfrac{d}{dx}right)^3$ obtains $sum_{n=1}^infty n^3x^n$. Now set $x=frac{1}{3}$.

share|cite|improve this answer

answered Mar 10 at 21:31

J.G.J.G.

30.1k23048

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  (+1) Although, I do not like the notation $(xfrac{d}{dx})^3$ 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 $(xfrac{d}{dx})^3$ mean?
  $endgroup$
  – Pink Panther
  Mar 10 at 21:38
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @PinkPanther It means three times - in this case, the operator $xfrac{d}{dx}$.
  $endgroup$
  – J.G.
  Mar 10 at 21:41
  

  
  
  
  

add a comment | 

2

$begingroup$

If $|x|<1$, $sum_{n=1}^infty x^n=frac{x}{1-x}$. Applying $left(xfrac{d}{dx}right)^3$ obtains $sum_{n=1}^infty n^3x^n$. Now set $x=frac{1}{3}$.

share|cite|improve this answer

answered Mar 10 at 21:31

J.G.J.G.

30.1k23048

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  (+1) Although, I do not like the notation $(xfrac{d}{dx})^3$ 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 $(xfrac{d}{dx})^3$ mean?
  $endgroup$
  – Pink Panther
  Mar 10 at 21:38
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @PinkPanther It means three times - in this case, the operator $xfrac{d}{dx}$.
  $endgroup$
  – J.G.
  Mar 10 at 21:41
  

  
  
  
  

add a comment | 

$begingroup$

If $|x|<1$, $sum_{n=1}^infty x^n=frac{x}{1-x}$. Applying $left(xfrac{d}{dx}right)^3$ obtains $sum_{n=1}^infty n^3x^n$. Now set $x=frac{1}{3}$.

share|cite|improve this answer

answered Mar 10 at 21:31

J.G.J.G.

30.1k23048

$endgroup$

share|cite|improve this answer

answered Mar 10 at 21:31

J.G.J.G.

30.1k23048

answered Mar 10 at 21:31

J.G.J.G.

30.1k23048

answered Mar 10 at 21:31

J.G.J.G.

30.1k23048