Hi, I'm having a little bit trouble applying the Monotone Sequence Theorem to this question:

Determine if the sequence defined by the recursive relation:

has a limit. Present your reasoning by using the Monotone Sequence Theorem.

Thanks a lot!

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- October 14th 2010, 01:13 PMAKTiltedProve the limit of this sequence exists
Hi, I'm having a little bit trouble applying the Monotone Sequence Theorem to this question:

Determine if the sequence defined by the recursive relation:

has a limit. Present your reasoning by using the Monotone Sequence Theorem.

Thanks a lot! - October 14th 2010, 01:43 PMPlato
Use induction to show that .

- October 14th 2010, 10:17 PMchisigma
The difference equation that defines the sequence can be written as...

(1)

The function is represented here...

http://digilander.libero.it/luposabatini/MHF78.bmp

There is only one 'attractive fixed point' in and, because for any is , any will produce a sequence that converges monotonically at ...

Kind regards

Kind regards