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) are coefficients in the binomial expansion of (1 + x)^(n) and n is even , then C_(0)^(2)-C_(1)^(2)+C_(2)^(2)+C_(3)^(2)+...+ (-1)^(n)C_(n)""^(2) is equal to .

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 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

If C_(0),C_(1),C_(2),C_(3), . . .,C_(n) be binomial coefficients in the expansion of (1+x)^(n) , then Q. The value of the expression C_(0)+2C_(1) +3C_(2)+. . . .+(n+1)C_(n) is equal to

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_(3), . . .,C_(n) be binomial coefficients in the expansion of (1+x)^(n) , then Q. The value of the expression C_(0)-2C_(1)+3C_(2)-. . . .+(-1)^(n)(n+1)C_(n) 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_(0)""^(2) + 2 C_(1)""^(2) + 3C_(2)""^(2) + ...+ (n +1)C_(n)""^(2) =

If C_0,C_1,C_2,.......,C_n denote the binomial coefficients in the expansion of (1+1)^n, then sum_(0ler) sum_(< s le n) (C_r+C_s)

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)) .