Given with

Show that is monotone.

I'm getting trouble to do that. It's a part of another problem which says to prove that converges, so in order to do that, I already proved that is bounded below.

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- Apr 3rd 2011, 04:28 PMConnectedMonotone sequence
Given with

Show that is monotone.

I'm getting trouble to do that. It's a part of another problem which says to prove that converges, so in order to do that, I already proved that is bounded below. - Apr 3rd 2011, 07:01 PMDrSteve
Do you mean ?

- Apr 4th 2011, 06:18 AMConnected
No, it's as is written.

Do you think there's a typo? - Apr 4th 2011, 06:47 AMDrSteve
There must be. Otherwise the sequence is constant for n>0.

- Apr 4th 2011, 07:03 AMHartlw
A constant sequence is monotonic. And Converges.

- Apr 4th 2011, 09:47 AMDrSteve
This particular sequence may or may not be monotonic. The given equation may have 2 solutions (depending on b), and therefore the given sequence isn't well defined - it could take on one of these values, or bounce between the 2. In any case, it is more likely that the problem has a typo.

- Apr 4th 2011, 12:14 PMHartlw
yn is either a real or complex constant depending on b. in either case its constant, monotonic (absoluteley if b complex), and convergent.