Real Analysis/Section 2 Exercises/Answers

On SequencesEdit

Problem 1Edit

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.

     

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

     

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

GeneralEdit

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