Discrete Math Question: Induction

Define a sequence recursively as follows. ${x}_{1}=1$ and for $n\in N,{x}_{n+1}=\sqrt{({x}_{n}{)}^{2}+1/({x}_{n}{)}^{2}}$

Prove using mathematical induction that for all $n\in N$, $1\le {x}_{n}\le \sqrt{n}$

Define a sequence recursively as follows. ${x}_{1}=1$ and for $n\in N,{x}_{n+1}=\sqrt{({x}_{n}{)}^{2}+1/({x}_{n}{)}^{2}}$

Prove using mathematical induction that for all $n\in N$, $1\le {x}_{n}\le \sqrt{n}$