- We need to establish if it's monotone, and what kind (is it strictly increasing, strictly decreasing, non-increasing, non-decreasing, what?). Given the problem, we'll assume strictly increasing.
- First, we should prove the base case. This means proving that a1 < a2.
- Next, we should prove that this works for any number n
- You're done! Everything checks out and is valid.
For problem 2, we see that supx_n =1 since n/(n+1) gets close to 1.