Data Structures and Algorithms -- 66-230
Discrete Mathematics Overview -- Class Exercise 3 on Summations

Here is the solution to the 3rd class exercise on summations:

$$\begin{align*} \sum_{i=1}^N \frac{i}{2^i} = S &= \frac{1}{2^1} + \frac{2}{2^2} +... ...\ &= \frac{(1/2)^N -1 }{-1/2} - \frac{N}{2^N} = 2 - \frac{N+2}{2^N}\end{align*}$$