The sum _k=1^20k2^k is equal to:

Question

The sum $\displaystyle\sum_{k=1}^{20}\dfrac{k}{2^k}$ is equal to:

Accepted Answer

Using the standard finite arithmetico-geometric sum $\displaystyle\sum_{k=1}^{n}\frac{k}{2^k} = 2 - \frac{n+2}{2^n}$:

$$\sum_{k=1}^{20}\frac{k}{2^k} = 2-\frac{22}{2^{20}} = 2-\frac{11}{2^{19}}.$$

Solutions · 1