Sunday, 11 May 2014

Find limit of recursive sequence

$0 \leq a\leq \frac{1}{4}$



$a_{1} = a,$ $a_{n+1} = a + (a_{n})^{2}$




I have to prove that the sequence has a limit, and to find the limit $a_{n}$.



Actually, I have no idea what to do.
I just know that the sequence is monotonic increasing, and I dont know why, i think that the lim is $a$.
Thanks.

No comments:

Post a Comment

real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...