I'm currently working on this problem:
At first, this looked like a pretty straightforward induction problem. But, once I started working on (b), I ran into an issue.
I can show that my base case is greater than or equal to 2, and then I assume for some n in N that x sub n is greater than or equal to 2. Next, I want to show that x sub n+1 is greater than or equal to 2, and I planned to do so with a simple series of inequalities. However, the 1/(x sub n) in the recursive definition is causing difficulty for me because it breaks my inequality.
Can someone give me some pointers here? Thanks!