A sequence of real numbers satisfies the recurrence relation
for all positive integer .
a) Given that converges to , find the value of
b) If , show that
I was able to find that for part a.
For (b), what I have done is:
How do I continue? Or am I going in the wrong direction?
The recurrence relation can be written as...
As explained in...
... has only one 'atrractive fixed point' in and because for all x is all initial value will produce a sequence monotonically convergent to 2...
Good question. I just solved the inequality and found that it is equivalent to , so in particular the latter implies the former.
I have a feeling that solving two inequalities to prove and is repeating some work, but to understand it better I probably need to read chisigma's tutorial...