If `(1+x)^n=C_0+C_1x+C_2x^2++C_n x^n` , then show that the sum of the products of the coefficients taken two at a time, represented by `sumsum_(0lt=i

If (1+x)^n=C_(0)C_1c+C_(2)x^2+…..+C_(n)x^n then show that the sum of the products of the C_(i) taken two at a time represented by : Sigma_(0 le I lt) Sigma_( j le n) C_(i)C_(j) "is equal to " 2^(2n-1)-(2n!)/(2.n! n !)

If (1+x)^n = C_0 + C_1x + C_2x^2 + ……..+C_n.x^n then find C_1 - C_3 + C_5 + ……

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 + …….

If (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , find the values of the following (sumsum)_(0leilt j le n)jC_(i)

If (1 + x + x^2)^n = C_0 + C_1x + C_2x^2 + C_3x^3 + ……..C_nx^n then find C_0 + C_3 + C_6 + …….

If (1+x)^n=C_0+C_1x+C_2x^2=……..+C_nx^n show that sum_(r=0)^(n-3) C_r C_(r+3) = ((2n)!)/((n+3)!(n-3)!)

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then the value of sumsum_(0lerltslen)(C_(r)+C_(s))^(2) is :

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then the value of sumsum_(0lerltslen)(r+s)(C_(r)+C_(s)) is :

If (1 + x)^(n) = C_(0) = C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , find the values of the following underset(0leile jlen)(sumsum)C_(i)C_(j)

If (1+x)^n=C_0+C_1x+C2x2++C_n x^n , n in N ,t h e nC_0-C_1+C_2-+(-1)^(n-1)C_(m-1), is equal to (mltn)