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## Homework Statement

Define a

_{1}=1, and for every n>1, a

_{n+1}= a

_{n}+ [itex]\frac{1}{a

_{n}}[/itex]. Prove that 20 < a

_{200}< 24

## The Attempt at a Solution

I tried a few things to no avail. First, I showed that this is an increasing function by showing a

_{n+1}> a

_{n}. I tried finding a limit, by saying if lim[itex]_{n\rightarrow∞}[/itex]a

_{n}= L then lim[itex]_{n\rightarrow∞}[/itex]a

_{n+1}= L. Plugging in L, and solving but that didn't help. I feel like I need to find an upper and lower bound and work from there but I'm not sure how