Finite sum k*x^k

Question

Prove that $$\sum_{k=0}^m k x^k = \frac{x(mx^{m+1}-(m+1)x^m +1)}{(x-1)^2}$$

Answer 1

Note that $$\sum_{k=0}^mkx^k=x\frac{d}{dx}\sum_{k=0}^mx^k$$

Answer 2

HINT :

Can you calculate $$ \sum_{k=0}^{m}x^k ? $$