some questions on convergence of sequences

Let be a sequence.

(i) Prove that if converges, then also converges.

(ii) Prove that if converges and , then converges.

For (i), can i use the concept of subsequences to tackle this question.

For (ii), how do I start this question?

Thanks in advance!(Wink)

Re: some questions on convergence of sequences

Quote:

Originally Posted by

**alphabeta89** Let

be a sequence.

(i) Prove that if

converges, then

also converges.

I'm not sure this is true. What happens if , then converges but I don't think does.

CB

Re: some questions on convergence of sequences

Quote:

Originally Posted by

**CaptainBlack** I'm not sure this is true. What happens if

, then

converges but I don't think

does.

CB

hmm? I think it still works for this sequence.

Re: some questions on convergence of sequences

Anyone has any idea on starting this question?