Find the value of: ∑∑ (i. nCj + j. nCi) 1≤ i < j ≤ n NOTE: i. nCj is i multiplied by n choose j
In that sum, each integer from 1 to n is multiplied by each binomial coefficient (k going from 1 to n), except for the "diagonal" products . So the sum is equal to . But , and . Therefore .