Finite sum k*x^k [closed]

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

closed as off-topic by Gabriel Romon, rae306, Henrik, Sri-Amirthan Theivendran, N. F. TaussigMay 15 '18 at 20:33

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Note that $$\sum_{k=0}^mkx^k=x\frac{d}{dx}\sum_{k=0}^mx^k$$
Can you calculate $$\sum_{k=0}^{m}x^k ?$$