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The arithmetic mean of ""^(n)C(0),""^(n)...

The arithmetic mean of `""^(n)C_(0),""^(n)C_(1),""^(n)C_(2), ..., ""^(n)C_(n)`, is

A

`(2^(n))/(n)`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Since, expansion contains `(n+1)` terms,
`"Required mean"=(.^(n)C_(0)+.^(n)C_(1)+^(n)C_(2)+.......+.^(n)C_(n))/((n+1))`
`=(2^(n))/(n+1)`
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