Real Analysis/Section 2 Exercises/Answers

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On Sequences[edit]

Problem 1[edit]

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.


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