Three questions, hope that's not too many!
1. I need to prove that the sequence
What I have is for any there exists such that
I take that as
Here is my first question: when I put that into
I need a fixed vaule for . What am I missing?
Prove that every unbounded sequence contains a monotone subsequence that diverges to infinity.
On this one, I know unbounded can mean divergent. What do I do next to prove this? I am confused on this one!
Prove that if a sequence converges to 0, and a sequence is bounded, then the sequence converges to 0.
I had gotten help on this before, but hadn't gotten very far. I'm starting with
, but how would I put this into a proof for this? again, confused!
Thanks in advance, and I might have some more later!