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=iltjlt=n) ``"^nc_i``"^n c_j` is equal to `2^(2n-1)-((2n)!)/ (2(n !)^2)`

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+......+C_(n)x^(n) then show that the sum of the products of the coefficients taken two at a time,represented by sum sum_(0<=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 !)

Find the sum sumsum_(0lt=ilt=jlt=n)^ nC_i^n C_j

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) +.................+ C_(n)x^(n) then show that the sum of the products of the C_(i)'s taken two at a time represents by : {:(" "sum" "sum" " c_(i)c_(j)),(0 le i lt j le n ):} is equal to 2^(2n-1)-(2n!)/(2.n!.n!)

If (1+x)^n=C_0+C_1x+C_2x^2+…..+C_nx^n .then show that C_1+2C_2+…. nC_n=n.2^(n-1) .

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_nx^n prove that : C_0+ 2C_1 +.........+2""^nC_n=3^n .