Compute the following (in Description below). Assume the value of n is restricted so that the expression is defined.

Question

Answer 1

Define B(n,k) = n!/(k! (n-k)!) as the binomial coefficient. We can find the desired expression to be equal to

B(n+1,n-1) = (n+1)!/((n-1)! 2!) = n(n+1)/2