If `(1 + x)^n = C_o + C_1 x+C_2 x² + ... + C_n x^n,` then the value of `1^2 C_1 +2^2 C_2+3^2 C_3 + ... ..`

If (1+x)^(n)=C_(o)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n) then the value of 1^(2)C_(1)+2^(2)C_(2)+3^(2)C_(3)+...

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

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 + 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.....

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+2. C_1 +3. C_2 +….+(n+1) . C_n=

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+ . . .+C_(n)x^(n) , then the value of : C_(1)+2C_(2)+3C_(3)+ . . .+nC_(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 (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 (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)