Prove that is strictly increasing for . Or in other words the recurrence equation is strictly increasing.

Printable View

- April 12th 2008, 04:39 AMjames_bondProve that it's strictly increasing
Prove that is strictly increasing for . Or in other words the recurrence equation is strictly increasing.

- April 12th 2008, 05:07 AMMoo
Hello,

Let's show that

And i have a problem oO - April 12th 2008, 07:40 AMMathstud28If
- April 12th 2008, 07:49 AMMoo
I derivated but it didn't give something interesting ;)

- April 12th 2008, 08:59 AMMathstud28Desole
- April 12th 2008, 09:03 AMMoo
You have to study the sign of the derivative. Well, good luck ^^ I've found it easier to study but can't conclude (just too lazy maybe)

- April 12th 2008, 09:24 AMMathstud28Haha
- April 28th 2008, 06:54 PMJaneBennet
Let

Then and*N*is strictly increasing is strictly increasing.

Let

Then

This is positive for all because both and .

Hence is strictly increasing.