If `C_r` stands for `nC_r,` then the sum of first `(n+1)` terms of the series `a C_0-(a+d)C_1+(a+2d)C_2-(a+3d)C_3+......,` is

The sum to (n+1) terms of the series C_0/2-C_1/3+C_2/4-C_3/5+......=

If C_r stands for nC_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 integer, is

If C_r stands for nC_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 integer, is

If C_r stands for nC_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 integer, is

If C_(r) stands for nC_(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 integer,is

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:

If n is a positive integer such that (1+x)^n=^nC_0+^nC_1+^nC_2x^2+…….+^nC_nx^n , for epsilonR . Also .^nC_r=C_r On the basis of the above information answer the following questions The value of the expression a-(a-1)C_1+(a-2)C_2-(a-3)C_3+.......+(1)^n(a-n)C_n= (A) 0 (B) a^n.(-1)^n.^(2n)C_n (C) [2a-n(n+1)].^(2n)C_n (D) none of these