1. ## summation identity proof

I have been trying to find a proof for the following summation identity.

$\sum_{n=0}^{\infty} nx^{n-1}=\frac{1}{(1-x)^2}$

I have found that we can prove this using the differentiation, but was wondering if there is another way to prove that, i.e., without using the differentiation

2. Originally Posted by led5v
I have been trying to find a proof for the following summation identity.

$\sum_{n=0}^{\infty} nx^{n-1}=\frac{1}{(1-x)^2}$

I have found that we can prove this using the differentiation, but was wondering if there is another way to prove that, i.e., without using the differentiation
Binomial expansion of (1-x)^(-2) followed by a bit of simplification should do it.

RonL