If `C_0, C_1,C_2………..C_n` be the coefficients of expansion (1+x)^n` prove that C0C2+C1C3+C2C4+C_n2n= 2n! /(n-2)! (n+2)!

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) are the binomial coefficients in the expansion of (1 + x)^(n) , prove that (C_(0) + 2C_(1) + C_(2) )(C_(1) + 2C_(2) + C_(3))…(C_(n-1) + 2C_(n) + C_(n+1)) ((n-2)^(n))/((n+1)!) prod _(r=1)^(n) (C_(r-1) + C_(r)) .

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 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_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 are binomial coefficients int eh expansion of (1+x)^n then and n is even, then C_0^2-C_1^2+C_2^2-C_3^2 + ... +(-1) C_n^2 , is equal to

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

If C_0, C_1,C_2 ..., C_n , denote the binomial coefficients in the expansion of (1 + x)^n , then C_1/2+C_3/4+C_5/6+...... is equal to

If C_0, C_1,C_2 ..., C_n , denote the binomial coefficients in the expansion of (1 + x)^n , then C_1/2+C_3/4+C_5/6+...... is equal to