Hey, I'm stuck on this question and desperately need help.
Suppose that the sequence is convergent, and assume that the sequence is bounded. Prove that the sequence defined by
is convergent and find its limit. (n belongs to the set of natural numbers)
Please help! I tried using the theorem that if a sequence is convergent, then it is bounded (for ) but get anywhere. :( It's quite clear to me that the limit is but I don't know how to get there.
Ok, thank you. :)
In the seminars, we haven't been told that if the sequence is bounded. As obvious as it is. :p
So do you think it would be more 'rigorous' if I said that since is bounded, there exists an such that
Then I can show that and . Since , then by the sandwich theorem,
Is that fine, in your opinion, or unnecessary?
That is excellent.
Originally Posted by Joel24