suppose we have
I'd like to show that as if
Now, this seems quite obvious maybe...as if
But how can we see ?
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??
The (1) can be written as...
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...
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?