Prove that the sequence converges.

I know it converges to 1. We need to use the definition of sequence convergence:

Another thing, obviously since

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- Apr 30th 2010, 02:18 PMsantiagos11prove that a sequence converges
Prove that the sequence converges.

I know it converges to 1. We need to use the definition of sequence convergence:

Another thing, obviously since - Apr 30th 2010, 02:58 PMPlato
- Apr 30th 2010, 03:36 PMsantiagos11
Well, you are certanly right. But how does that fit the standard definition?

- Apr 30th 2010, 04:02 PMPlato
- Apr 30th 2010, 05:04 PMsantiagos11
For example, here is a partial proof:

Let . Clearly

case 1:

Let . Suppose . Then . On the other hand , so . Therefore, .

Do you see how this follows the definition that I gave in the top?

Now it remains to show the same, in the case - Apr 30th 2010, 06:15 PMPlato
- May 1st 2010, 06:48 PMsantiagos11
Well yeach I gues you are right. However I do have another problem:

Prove that that the following sequence,defined recursively, converges or diverges: