It would be better to prove it By using the Second Mathematical Induction(change the inductive hypothesis to )
Show that for all real values of the variables. Furthermore, give a condition for equality to hold.
Base case:
Let
Which is true because of Cauchy-Schwarz.
Inductive Hypothesis:
Assume the inequality is true for
is true.
Proof:
Need to prove it's true for
So let's add to our inductive hypothesis.
This yields:
now what?