I have a simple question. Does there exists a finite constant , Such that the sequence , defined by the iteration :
Not converges to any single finite value for
What inspires me to ask this is the analysis I have done on my laptop :
What I did is that for different values of , I calculated such that gets within the value of . I got this :
And the last one is :
Also when I tried for , it just won't show any value for half an hour.
It is very weird as rate of converge gets immediately slow and I believe convergence must stop at some value of .
I don't know can someone do a computer analysis of this, or tell me the maths of the underlying situation.