1. The problem statement, all variables and given/known data Let n, k be in the set of all positive integers including zero. Define (n k)=n!/k!(n-k)! Determine the value of [itex]\sum[/itex] (n k) from k=0 to n. Determine the value of [itex]\sum[/itex] (n k) from k=0 to n. 3. The attempt at a solution I tried evaluating for some n value: (n 0)= 1 (n 1)= n (n 2)= (1/2!)n(n-1) (n 3)= (1/3!)n(n-1)(n-2) So, generally= 1+n+......+[(1/k!)(n)*.....*(n-(n-k))]+1 Am I on the right track? How can I determine the value? Any help is appreciated.