Sum of the products of the binomial coefficients `C_0,C_1,C_2,......C_n` taken two at a time is:

Sum of the products of the binomial coefficients of (1+x)^(n) taken two at a time is

Sum of the products of the binomial coefficients of (1+x)^(n) taken two at a time is

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_(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 C_(0), C_(1), C_(2), …, C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then sum_(0 ler )^(n)sum_(lt s len)^(n)C_(r)C_(s) =.