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The A.M of the series 1, 2, 4, 8, 16…., ...

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

A

`(2^(n)-1)/(n)`

B

`(2^(n+1)-1)/(n+1)`

C

`(2^(n)+1)/(n)`

D

`(2^(n)-1)/(n+1)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`
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