Question

Evaluate the following

$n\sum i=1 (3/2^(i-1))$

Answer 1

The aim is to compute the sum: $n\sum_{i=0}^ni$. The sum $\sum_{i=0}^ni$ is an arithmetic progression. It is a well-known formula. $n\sum_{i=0}^ni=n(0+1+2+\ldots+n)=n\left(\frac{n(n+1)}{2}\right)=\frac{n^2(n+1)}{2}.$