The AM of the series 1, 2, 4, 8, 16, ... , 2n, is
2n−1n
2n+1−1n+1
2n+1n
2n−1n+1
The required AM is given by
X¯=1+2+22+23+…+2nn+1=2n+1−1(n+1)(2−1)=2n+1−1n+1