Given a:
$a_0>0$, and $a_{n+1}=\sin(a_n)$.
I need to prove that the sequence $a_{n=0}^\infty$ converges, then calculate the limit.
I have proved that is crescent, then I got stuck.
Asked
Active
Viewed 30 times
0
Lisandro Di Meo
- 45
- 8
-
1This is likely a problem that has been solved here previously. I'll see if I can find a duplicate for you. When you say "I have proved that is crescent", I suspect what you mean is *contractive" (with respect to the function $\sin x$ that is repeatedly applied). Can you clarify what exactly you did prove? – hardmath Aug 28 '18 at 04:43
-
1...also duplicate of How find this limit $\lim_{n\to\infty}\underbrace{\sin{\sin{\cdots\sin{x}}}}_{n},x\in R$, Limit of infinite loops of sin x as n tends to infinity. – dxiv Aug 28 '18 at 04:56