If`C_0+C_1+C_2+.........+C_n = 128`, then `C_0 -(C_1)/2+(C_2)/3 -(C_3)/4+........ =`

C_0+C_1+C_2+.........+C_(N-1)+C_N=

If (1 + x + x^2)^n = (C_0 + C_1x + C_2 x^2 + ............) then the value of C_0 C_1-C_1C_2+C_2C_3.....

C_0 + 2.C_1 + 4.C_2 + …….+C_n.2^n = 243 , then n =

If C_(0),C_(1),C_(2)…….,C_(n) are the combinatorial coefficient in the expansion of (1+x)^n, n, ne N , then prove that following C_(1)+2C_(2)+3C_(3)+..+n.C_(n)=n.2^(n-1) C_(0)+2C_(1)+3C_(2)+......+(n+1)C_(n)=(n+2)C_(n)=(n+2)2^(n-1) C_(0),+3C_(1)+5C_(2)+.....+(2n+1)C_n =(n+1)2^n (C_0+C_1)(C_1+C_2)(C_2+C_3)......(C_(n-1)+C_n)=(C_0.C_1.C_2....C_(n-1)(n+1)^n)/(n!) 1.C_0^2+3.C_1^2+....+ (2n+1)C_n^2=((n+1)(2n)!)/(n! n!)

If (1+x)^n=C_0+C_1x+C_2x^2+...+C_n x^n , t h e n 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_(n-1)) , where n a) is even integer b) is a positive value c) a negative value d) divisible by 2^(n-1) divisible by 2^n

If (1 + x)^n = C_0+C_1x+C_2x^2 + ... + C_nx^n ,then for n odd, 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) , 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_(n-1)) is (where n is even integer and C_(r) = .^(n)C_(r) )

If C_(0), C_(1), C_(2),..., C_(n) are binomial coefficients in the expansion of (1 + x)^(n), then the value of C_(0) + (C_(1))/(2) + (C_(2))/(3) + (C_(3))/(4) +...+ (C_(n))/(n+1) is

If C_(0), C_(1) C_(2) ….., denote the binomial coefficients in the expansion of (1 + x)^(n) , then (C_(0))/(2) - (C_(1))/(3) + (C_(2))/(4)- (C_(3))/(5)+...+ (-1)^(n)(C_(n))/(n+2) =

If (1+x)^n = C_0 + C_1x + C_2x^2 + ……..+C_n.x^n then find C_0 - C_2 + C_4 - C_6 + …….