Explanation:
We first prove the base case, which is proving that the inequality holds for n=2:

So
and base case is proven.
We then do the inductive step, which is assuming that the inequality holds for n=k, and proving out of that that the inequality also holds for n=k+1:
Assume the inequality holds for n=k. This means that

Our goal is then to show that
.
We have that

(since we're assuming that
, we know that
).
So
, and the inductive step is proven.
Therefore we can conclude by the principle of mathematical induction that for all 