The question is:
$0\leq\alpha\leq \frac{1}{4}$, We'll define $a_1=\alpha$, $a_{n+1}=\alpha+a_n^2$. Prove $(a_n)_{n=1}^\infty$ is converging and find it's limit.
I'm really confused about it, so I tried taking the private case of $\alpha=\frac{1}{4}$ but I still don't really understand it.
$a_1=\frac{1}{4}$
$a_2=\frac{5}{16}$
$a_3=\frac{89}{256}$
And I'm not really sure where this is going to or what I'm supposed to do with it.