Suppose that and for all Prove that this sequence converges and find its limit.

I was hoping that I could avoid induction on this one but I don't know any other method to prove this.

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- Feb 6th 2010, 12:16 PMEm Yeu AnhProve this sequence converges
Suppose that and for all Prove that this sequence converges and find its limit.

I was hoping that I could avoid induction on this one but I don't know any other method to prove this. - Feb 6th 2010, 01:12 PMtonio
- Feb 6th 2010, 01:18 PMfelper
You can prove that the sequence is crecent and is bounded. To calculate the limit, you can use that the subsequences of a sequences converges to the same limit. Then,