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## Homework Statement

1) [tex] \displaystyle \sum\limits_{n=1}^{\infty }{\frac{{{n}^{3}}}{{{e}^{n}}}}[/tex]

2) [tex] \displaystyle \sum\limits_{n=1}^{\infty }{\frac{-1}{2\left( n+1 \right)}+\frac{2}{\left( n+2 \right)}-\frac{3}{n\left( n+3 \right)}}[/tex]

## Homework Equations

## The Attempt at a Solution

I've proved that both series converge. In fact the second series was given like this:

[tex] \displaystyle \sum\limits_{n=1}^{\infty }{\frac{n}{\left( n+1 \right)\left( n+2 \right)\left( n+3 \right)}}[/tex]

I just simplified to calculate the sum. Anyway, I don't know how to do that. I don't know when I am able to split the series into sum of series because I know that it cannot be done sometimes but sometimes it can.

Thanks