If`C_0,C_1,C_2..C_n` denote the coefficients in the binomial expansion of `(1 +x)^n`, then `C_0 + 2.C_1 +3.C_2+. (n+1) C_n`

If C_0,C_1,C_2...C_n denote the coefficients in the binomial expansion of (1+x)^n, prove that C_0+3C_1+5C_2+...+(2n+1)C_n=(n+1)2^n

If C_(0),C_(1), C_(2),...,C_(n) denote the cefficients in the expansion of (1 + x)^(n) , then C_(0) + 3 .C_(1) + 5 . C_(2)+ ...+ (2n + 1) C_(n) = .

If C_(0),C_(1), C_(2),...,C_(n) denote the cefficients in the expansion of (1 + x)^(n) , then C_(0) + 3 .C_(1) + 5 . C_(2)+ ...+ (2n + 1) C_(n) = .

If C_o, C_1, C_2 ....,C_n C denote the binomial coefficients in the expansion of (1 + x)^n, then 1^3. C_1 + 2^3 . C_2 + 3^3 .C_3 + ... + n^3 .C_n, =

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1. C_(1) - 2 . C_(2) + 3.C_(3) - 4. C_(4) + ...+ (-1)^(n-1) nC_(n)=

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1. C_(1) - 2 . C_(2) + 3.C_(3) - 4. C_(4) + ...+ (-1)^(n-1) nC_(n)=

If C_0, C_1, C_2 ,……..C_n are the coefficient in the expansion of (1 + x)^n then show that C_0 C_r + C_1 C_(r + 1) + C_2 C_(r + 2) + ………..+ C_(n-r).C_n = ((2n)!)/((n-r)!(n+r)!)

If C_(0), C_(1), C_(2),...,C_(n) denote the binomial coefficients in the expansion of (1 + x)^n) , then xC_(0)-(x -1) C_(1)+(x-2)C_(2)-(x -3)C_(3)+...+(-1)^(n) (x -n) C_(n)=

If C_(0), C_(1), C_(2),...,C_(n) denote the binomial coefficients in the expansion of (1 + x)^n) , then xC_(0)-(x -1) C_(1)+(x-2)C_(2)-(x -3)C_(3)+...+(-1)^(n) (x -n) C_(n)=