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

Sum of first half binomial coefficients

Sum of the products of the binomial coefficients C_(0),C_(1),C_(2),......C_(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 n be a positive integer and P_(n) denotes the product of the binomial coefficients in the expansion of (1+x)^(n), prove that (P_(n+1))/(P_(n))=((n+1)^(n))/(n!)

Find the sum of the product of the integers 1,2,3…..n taken two at a time and over the sum of their squares.

Series Involving Product of Two Binomial Coefficients

Series Involving Product of Two Binomial Coefficients