- #1

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## Homework Statement

I feel bad asking another question after I just asked one yesterday, but I'm really close this time, I think!

I have:

[tex]\sum_{n=2}^{\infty}\frac{n^2-n}{2^n}[/tex]

And need to find the sum.

## Homework Equations

[tex]\sum_{n=1}^{\infty}nx^{n-1}=\frac{1}{(1-x)^2}[/tex]

## The Attempt at a Solution

I have refectored this sum into the form:

[tex]\sum_{n=1}^{\infty}\frac{n^2+n}{2^{n+1}}[/tex]

and can then split it into its two terms.

When finding the sum of the term [itex]\frac{n}{2^{n+1}}[/itex] by factoring out 1/4 and using the formula above, I get 1/4, however, when the sum should be 1. Am I not applying this formula properly?

Additionally, how can I apply the above formula to the term [itex]\frac{n^2}{2^{n+1}}[/itex]? I can again factor out 1/4, but then I'm left with an n

^{2}rather than n.

Guidance for any of these steps would be awesome!