Problem
ALG-B1-M05-P015 Recurrence and Boundedness
#15
★★★★★ Level 5 of 5
Let \(0
Consider \(1-a_{n+1}\).
\(1-a_{n+1}=1-2a_n+a_n^2=(1-a_n)^2\). If \(0 Also \(a_{n+1}-a_n=a_n(1-a_n)>0\). Therefore the sequence is increasing.
A useful substitution around the limit \(1\).