## On Sequences

### Problem 1

Strictly Increasing:

1. 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.
2. First, we should prove the base case. This means proving that a1 < a2.

{\displaystyle {\begin{aligned}a_{1}&

3. Next, we should prove that this works for any number n

{\displaystyle {\begin{aligned}a_{n}&

4. You're done! Everything checks out and is valid.

## General

For problem 2, we see that supx_n =1 since n/(n+1) gets close to 1.