Finite sum k*x^k

Question

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

Possible duplicate of How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$? — N. F. Taussig, May 15 '18 at 20:33

score 2 · Answer 1 · answered May 15 '18 at 20:29

2

HINT :

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

answered May 15 '18 at 20:29

Atmos

score 2 · Accepted Answer · answered May 15 '18 at 20:30

2

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

answered May 15 '18 at 20:30

Andrei

2 Answers2