Question

The arithmetic mean of the series $1,2,2^2,\dots {.2}^{n-1}$ is

Answer 1

$S_n=2^0+2^1+2^2+2^3.....{.2}^{n-1}$

$S_n=\frac{1(2^n-1)}{2-1}=2^n-1$

$Mean=\frac{2^n-1}{n}$ (as total number of terms are n)