Solving this summation: $\sum_{i=1}^k i\cdot2^i$ $$\sum_{i=1}^k i\cdot2^i$$
I'm working on a recurrence relation question and now I'm stuck at this point. I have no idea how to simplify this down to something I can work with.  Can I seperate the terms into
$$\sum_{i=1}^k i \cdot \sum_{i=1}^k 2^i$$ and then just use the geometric series? 

Let $S$=$\sum_{i=1}^k i\cdot2^i$
Consider $2S$=$\sum_{i=1}^k i\cdot2^{i+1}$.
Do $S-2S$ and the result is an G.P - an extra term $k2^{K+1}$.Find S.
