# Homework Help: Interesting convergence of sequence

1. Feb 13, 2012

### grusini

1. The problem statement, all variables and given/known data
Let $(a_n)_{n\in\mathbb{N}}$ be a real sequence such that $a_0\in(0,1)$ and $a_{n+1}=a_n-a_n^2$
Does $\lim_{n\rightarrow\infty}na_n$ exist? If yes, calculate it.

2. Relevant equations

3. The attempt at a solution
I have a solution but I'd like to see other solutions..

2. Feb 13, 2012

### Dick

Asking for a solution when you haven't shown your own goes against the general spirit of the homework help forum. Try another forum if you don't want to show your own proof.