Mathematical Induction

The sequence of real numbers $a_1$, $a_2$, $a_3$...is such that $a_1$ $=$ $1$ and $a_{n+1} = (a_n + \frac{1}{a_n} )^{\lambda}$
,where $\lambda$ is a constant greater than 1.

Prove by mathematical induction that for n ≥ 2,
$a_n$ ≥ $2^{g(n)}$ where $g(n)=\lambda^{n-1}$

Prove also that for $n\ge 2$, $\frac{a_{n+1}}{a_n}>2^{(\lambda-1)g(n)}$

This question is really confusing me. I cant even prove the base case