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If (1 + x)^(n) = C(0) + C(1)x + C(2) x^(...

If `(1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + …+ C_(n) x^(n)`, then for n odd,
`C_(1)^(2) + C_(3)^(2) + C_(5)^(2) +....+ C_(n)^(2)` is equal to

A

`2^(2n-2)`

B

`2^(n)`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + ... + C_(n) x^(n) , then value of C_(0)^(2) + 2C_(1)^(2) + 3C_(2)^(2) + ... + (n + 1) C^(2)n is

    A
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    `n.2^(n-1)`
    B
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    C
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    D
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