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