Originally Posted by

**simplysparklers** Hey guys!

I have 3 similar problems, if someone could please show me how to do one of them that would be great!

They all involve finding $\displaystyle \lim_{n\rightarrow\infty}$ of $\displaystyle a_{n}$, when $\displaystyle a_{n}$ isn't given.

1.) $\displaystyle a_{1}=0, a_{n+1}=\frac{3a_{n}+1}{a_{n}+3}$ $\displaystyle (n\geq{1})$

Find $\displaystyle \lim_{n\rightarrow\infty}a_{n}$

2.) $\displaystyle a_{1}=2, a_{n+1}=\frac{2a_{n}+3}{a_{n}+2}$ $\displaystyle (n\geq{1})$

Find $\displaystyle \lim_{n\rightarrow\infty}a_{n}$

3.) Determine the limit of $\displaystyle (a_{n})$, where

$\displaystyle a_{1}=2,a_{n+1}=\sqrt{2+2a_{n}}$ $\displaystyle (n\geq{1})$

If someone could show me how to do one of them I'd really appreciate it!!

Thanks,

Jo