Computing $\sum_{i=1}^k{i\cdot c^i}$ I would like to compute the following sum : 
  $$\sum_{i=1}^k{i\cdot c^i}$$
  where $k$ and $c$ are any real numbers.


I know how to compute $i$ and $c^i$ separately but I don't know how to do it when they are multiplied together.

Thanks a lot for the help!
Hint:

Do some analysis:
$$\sum_{i=1}^k ic^i=c\sum_{i=1}^kic^{i-1}=c\Bigl(\sum_{i=0}^k c^i\Bigr)'. $$
Hint: Let $a,q$ be real numbers with $q\ne 1$:
$$a + aq + aq^2 + \ldots +aq^{n-1} = a\frac{q^n-1}{q-1}.$$