For each
.
As you combine the inequalities, the right side will cancel out, leaving you with
.
Divide by to get the result.
We have the inequality for nonnegative . So using we have the left side of the inequality:
and the right side:
.
There are of these inequalities since . We add the inequalities together. For the left side, we will have
and the right side:
,
so
Divide both sides by to finish the proof.