I looked at $\frac{\sum 2i}{\sum2^i}$ (division), however both expressions are not equal. I am looking for an expression like $\sum_{i=1}^n\frac{2i}{2^i}=5n$ for example.
What is the closed form of $\sum_{i=1}^n\frac{2i}{2^i}$
$\begingroup$
sequences-and-series