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## Homework Statement

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.