- #1
Elysian
- 33
- 0
Homework Statement
Define a1=1, and for every n>1, an+1 = an + [itex]\frac{1}{an}[/itex]. Prove that 20 < a200 < 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 an+1 > an. I tried finding a limit, by saying if lim[itex]_{n\rightarrow∞}[/itex]an = L then lim[itex]_{n\rightarrow∞}[/itex]an+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