If `n` is a positive integer and `C_k = .^nC_k` then find the value of `sum_(k=1)^n k^3 * (C_k/C_(k-1))^2.`

If `n` is a positive integer and `C_k = .^nC_k` then find the value of `sum_(k=1)^n k^3 * (C_k/C_(k-1))^2.`
A. `(n(n+1)(n+2))/(12)`
B. `(n(n+1)^(2)(n+2))/(12)`
C. `(n(n+1)(n+2)^(2))/(12)`
D. none of these

If `n` is a positive integer and `C_k = .^nC_k` then find the value of `sum_(k=1)^n k^3 * (C_k/C_(k-1))^2.`

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