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
Since you're asked to prove a property for $n\ge 2$, the base case is the $n=2$ case: $$a_2\ge 2^{g(2)}$$ This is very easy (in fact trivial) to prove once you unfold the defintions of $a_2$ and $g(2)$.