`C_0 C_1 +C_1 C_2+C_2 C_3 +...+C_(n-1) C_n`

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3)x^(3) + …+ C_(n) x^(n) , then C_(0) - (C_(0) - C_(1)) + (C_(0) + C_(1) + C_(2))- (C_(0) + C_(1) + C_(2)+ C_(3)) + ...+ (-1)^(n-1) (C_0) + C_(1) + C_(2) + ...+ C_(n-1)) , when n is even integer is

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) C_n^2, is equal to

If (1+ x)^(n) = C_(0) + C_(1) x + C_(2)x^(2) + ...+ C_(n)x^(n) , prove that C_(1) + 2C_(2) + 3C_(3) + ...+ n""C_(n) = n*2^(n-1)

If C_(r) = ""^(n)C_(r) and (C_(0) + C_(1)) (C_(1) + C_(2)) … (C_(n-1) + C_(n)) = k ((n +1)^(n))/(n!) , then the value of k, is

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + ... + C_(n) x^(n) , then value of C_(0)^(2) + 2C_(1)^(2) + 3C_(2)^(2) + ... + (n + 1) C^(2)n is

If (1+x)^n = C_0 + C_1 x + C_2x^2 + …………+C_n x^n , find the value of C_0 - 2C_1 + 3C_2 - ……….+ (-1)^n (n+1) C_n

If C_(0), C_(1), C_(2), …, C_(n) are the coefficients in the expansion of (1+x)^(n) , then what is the value of C_(1) +C_(2) +C_(3) + …. + C_(n) ?