If Cr stands for ^nCr, then the sum of the series 2 (n/2)!(n/2)!/n! (C0^2 - 2C1^2 + 3C2^2 - .......+ (-1)^n (n+1)Cn^2)

Question

If C_r stands for ⁿC_r, then the sum of the series 

\(2\frac{(\frac n2)!(\frac n2)!}{n!} ({C_0}^2 - 2{C_1}^2+ 3{C_2}^2-....+(-1)^n (n+1) {C_n}^2)\) when n is an even positive integer, is equal to

(a) (–1)^n/2 (n + 2)

(b) (–1)ⁿ (n + 1)

(c) (–1)^n/2 (n + 1)

(d) None of these

Answer 1

(a) (–1)^n/2 (n + 2)