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If C(r) stands for ""^(n)C(r), then the ...

If `C_(r)` stands for `""^(n)C_(r)`, then the sum of the series `(2((n)/(2))!((n)/(2))!)/(n!)[C_(0)^(2)-2C_(1)^(2)+3C_(2)^(2)-...+(-1)^(n)(n+1)C_(n)^(2)]`, where n is an even positive integers, is:

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
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