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.
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.