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If the value of "^(n)C(0)+2*^(n)C(1)+3*^...

If the value of `"^(n)C_(0)+2*^(n)C_(1)+3*^(n)C_(2)+...+(n+1)*^(n)C_(n)=576`, then `n` is

A

`7`

B

`5`

C

`6`

D

`9`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `S=^(n)C_(0)+2.^(n)C_(1)+3.(n)C_(2)+...+(n+1).^(n)C_(n)`
Here `T_(r )=(r+1)^(n)C_(r )=n^(n-1)C_(r-1)+^(n)C_(r )`
`:.S=n^(2n-1)+2^(n)=576` (given)
`:.n=7`
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