Please see attached, Bounded Monotonic Convergence Theorem, Sequences

Question

anonymous · Answer

attachment

anonymous · Answer

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

anonymous · Answer

Need to do this using principle of mathematical induction

anonymous · Answer

You've shown that it's increasing already?

anonymous · Answer

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.

anonymous · Answer

That is what I was thinking too

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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