sorry, I need to add
I wonder how we can see ...as clearly is growing with such a starting value. But, why can it not converge
to some specific value a in (0.968,1)
edit: furthermore, is it even obvious that can not exceed the value 1??
Let's suppose to have the sigh instead of sigh so that the 'recursive relation' is...
(1)
The (1) can be written as...
(2)
The is represented here...
There are three zeroes in , and . and are both 'attractive fixed points' and is a 'repulsive fixed point'. Any will produce a sequence converging at and any will produce a sequence converging at . The case is left to You...
Kind regards
Thanks, I have another question. Dunno If I should make a new thread for this...this was actually part of an article I was reading. (and didn't quite understand all the details).
Suppose we have then we have as if
Then the following observation is made: . Now this very unclear to me...Can
we see from the recurrence relation that goes to 1 fast enough?