Question

Please see attached, Bounded Monotonic Convergence Theorem, Sequences

Answer 1

The part I am having trouble with is proving that the sequence is BOUNDED by some horizontal asymptote L...

Answer 2

Need to do this using principle of mathematical induction

Answer 3

You've shown that it's increasing already?

Answer 4

I don't think you NEED to prove that it's bounded. They tell you "assume Xn is in [1,5) for all n."
Seems to me like they're giving you that part for free.

Answer 5

That is what I was thinking too

Answer 6

The "Showing that it is increasing", I know how to do, but the bounded part, that is what I was assuming as well

Answer 7

Well, as I read this problem, they aren't even asking you to show that it converges. They are just asking for increasing, which would be a part of the proof that it converges.

Answer 8

Life lesson: don't do more than you have to. haha