- #1

- 10

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## Homework Statement

Prove (n choose k) ≤ ((en)/k)^k by induction on k.

## Homework Equations

I can't of anything that's awfully relevant besides the general steps of induction.

## The Attempt at a Solution

So I found it true for the k=1 case which was easy enough. Then assumed true the k case. And now have to prove the k+1 case.

So after working on the problem for awhile, I arrived at

((n-k)/(k+1)) * (n choose k) ≤ ((en)/k)^k * ((n-k)/(k+1))

but from here I'm stuck and not sure how to deconstruct the (n choose k) into something workable, let alone construct (n choose k+1). any help would be greatly appreciated.