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 sum Up (Posted on 2014-02-26)
Find the infinite sum of :: 13/31+23/32+33/33+43/34+...

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

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 Method for solution... | Comment 2 of 5 |

This is the series:

¡Ä

n=1

We can start with the fact that the infinite series x©ú = x / (1-x), and then differentiate a few times to end up with something of the form:

on the left hand side.  Then just substitute x = 1/3 to solve for the limit.  I've done it on paper and confirmed Charlie's solution.

Edit: Wow, the formatting appears to have gotten messed up.

I'll try again:

Start with the sum of the series x^n as n -> infinity.

Differentiate a few times until you end up with n^3 * x^n.

Plug in x = 1/3 to get the answer.

Edited on February 26, 2014, 1:13 pm
 Posted by tomarken on 2014-02-26 13:11:36

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