I need to obtain the sum of the following series(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \sum _{n=1} ^{\infty} \frac{n^2}{2^n} [/tex]

Well, with the aid of Mathematica, I get the answer, which is 6. What I'm trying to do now is work my way backwards from there. I need to express it through the geometric series

[tex] \sum _{n=0} ^{\infty} x^n = \frac{1}{1-x} [/tex]

In fact, my guess is that I should use

[tex] \sum _{n=1} ^{\infty} n x^{n-1} = \frac{1}{\left( x - 1 \right) ^2} [/tex]

but it can't get it to fit in.

Thank you very much.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding the Sum of a particular Power Series

**Physics Forums | Science Articles, Homework Help, Discussion**