I am trying to follow along on this proof of the Arithmetic-geometric mean inequality, but I pretty much crashed at a couple steps.
If $a_1 \leq G \leq a_n$, then why is it that $a_1 + a_n \geq \frac{a_1a_n}{G}+ G$?
Why do we remove $a_1$ in the induction hypothesis and put in $\frac{a_1a_n}{G}$ ?