The A.M. of the series `1, 2, 4, 8, 16,.....,2^n` is -

Options

A. `(2^(n)-1)/(n)`
B. `(2^(n+1)-1)/(n+1)`
C. `(2^(n)+1)/(n)`
D. `(2^(n)-1)/(n+1)`

Answer

B

Explanation

The required AM is
`overline(X)=(1+2+2^(2)+2^(3)+..+2^(n))/(n+1)=((2^(n+1)-1))/((n+1)(2-1))=(2^(n+1)-1)/(n+1)`