If `(1+x)^n=C_0+C_1x+C2x2++C_n x^n ,t h e nC_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_(n-1)),w h e r en` is even integer is a positive value a negative value divisible by`2^(n-1)` divisible by`2^n`

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 (1+x)^n = C_0 + C_1x + C_2x^2 + ………. + C_n x^n , prove that : C_0 + 2C_1 + ….. + 2 ""^nC_n = 3^n

If (1 + x)^(n) = C_(0) + C_(1) x C_(2) x^(2) +…+ C_(n) x^(n) , then the sum C_(0) + (C_(0)+C_(1))+…+(C_(0) +C_(1) +…+C_(n -1)) is equal to

If (1+x)^n = C_0 + C_1x + C_2x^2 + ………. + C_n x^n , prove that : C_0 + (C_1)/(2) + (C_2)/(3) + ……. + (C_n)/(n+1) = (2^(n+1) -1)/(n+1)

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 quad (1+x)^(n)=C_(0)+C_(1)x+C2x2++C_(n)x^(n),n in N,thenC_(0)-C_(1)+C_(2)-+(-1)^(n-1)C_(m-) is equal to (m

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