Hi. I am trying to prove the following:
1 + C(2n, 1) + C(2n, 2) + ... + C(2n, k) <= (2n)^k for n >= k > 1.
I would appreciate any suggestions you all may have.
Try to prove that P(k+1) will be valid if P(k) is valid.
There are k+1 terms in the numerator of the LHS and k+1 terms on the RHS, since there are k occurances of 2n.
It's easy to see that the inequality holds.