pisrationalhahaha
New member
- Joined
- Aug 22, 2017
- Messages
- 46
(x)n is a sequence defined by x0∈[0,1] and xn+1=1−xn2
Already proved that ∀n∈N,xn∈[0,1] (first part of the exercise)
The second part they asked to show that the two sequences (x2n) and (x2n+1) converge to different limits
The problem is that I never used to find limits of recurrent sequences whose first term is defined by an interval instead of a value
I'm stuck at this point never knowing what to do
I tried to study the function f(x)=1-x^2 which is decreasing on [0,1] and see if f(f((x2n))) is increasing or not....
Any hints ?
Already proved that ∀n∈N,xn∈[0,1] (first part of the exercise)
The second part they asked to show that the two sequences (x2n) and (x2n+1) converge to different limits
The problem is that I never used to find limits of recurrent sequences whose first term is defined by an interval instead of a value
I'm stuck at this point never knowing what to do
I tried to study the function f(x)=1-x^2 which is decreasing on [0,1] and see if f(f((x2n))) is increasing or not....
Any hints ?