Question

The arithmetic mean of the series $1,2,2^7,....{.2}^{n-1}$ is

• A. $\frac{2^n}{n}$
• B. $\frac{2^n-1}{n}$
• C. $\frac{2^{n+1}}{n}$
• D. None of these

Answer 1

The correct option is B $\frac{2^n-1}{n}$

Note : There is error in question. It shouls be
$1,2,2^2,....{.2}^{n-1}$
Sum of the series $2^0,2,2^2,....{.2}^{n-1}$
$\Rightarrow \frac{2^0(2^n-1)}{(2-1)}=2^n-1$
Arithmetic Mean $=\frac{2^n-1}{n}$