Evaluate the sum \(\frac{1}{2^1} + \frac{2}{2^2} + \frac{3}{2^3} + \cdots + \frac{k}{2^k} + \cdots \)
By telescoping sums, the sum is 5/2.
I know the answer is 2
but I do not know how to derive these equations to a final sum....anyone else?
Like so:
