Question

Show that if n and k are integers with 1 ≤ k ≤ n, then c(n,k)<=n^k/(2^(k-1)

Answer 1

sounds inductive ...

Answer 2

you know the formula for C(n,k) right?

Answer 3

yes, I do

Answer 4

I will give it a try by induction.Thanks though

Answer 5

not sure if an algebra would be sufficient ... maybe

Answer 6

I actually thought it requires a combinitorial proof.

Answer 7

im not proficient enough to even recall what a combinatorial proof entails :)
\[\frac{n!}{k!~(n-k)!}\le\frac{2n^k}{2^k}\]