So I have written down some notes, and I have forgotten why i wrote what i wrote down.

Find the sum of the series

$\displaystyle \sum_{n=1}^\infty nx^n$

I wrote down these steps

$\displaystyle \sum_{n=1}^\infty nx^n$= x$\displaystyle \sum_{n=1}^\infty nx^{n-1}$=x* $\displaystyle \frac{1}{(1-x)^2}$= $\displaystyle \frac{x}{(1-x)^2}$ for abs(x)<1

I don't know how they come about...