Please I need help solving this question:
$E(x)= \left \{ \left(1+ \frac{x}{n} \right)^n : n \in \mathbb{N} \right \}$. Let $a(x) = \sup E(x)$ (least upper bound).
(1)Prove that $a(x) < a(y)$ if $0 < x < y$.
(2) Prove that $a(x)a(y) \leq \left( a \left( \frac{x+y}{2} \right) \right) ^ 2$.
I already proved that E(x) has no largest element and is bounded and I proved part 1.
But I'm having trouble with the proof in part 2. Any help please?