If n is a positive integer and C(k)=""^(...

If n is a positive integer and `C_(k)=""^(n)C_(k)`, then the value of `sum_(k=1)^(n)k^(3)((C_(k))/(C_(k-1)))^(2)` is :

A

`(n(n+1)(n+2))/(12)`

B

`(n(n+1)^(2))/(12)`

C

`(n(n+2)^(2) (n+1))/(12)`

D

None of these

Verified by Experts

The correct Answer is:

D

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