** Claim: ** holds for all positive integers , and no others.

* Proof. * To show that it does not hold for we compute:

Now, for the case on the left we have

While, on the right we have,

Since 16 is indeed less than 24, we the inequality holds for . Assume then that the inequality holds for some . Then,

Where the last inequality uses the fact that since so . Thus, the inequality holds for the case ; and hence, for all