We define a sequence recursively in the following way.

$\displaystyle s_1=2$

and

$\displaystyle s_n=\sqrt{3+2_{s_{n-1}}}$ for $\displaystyle n>1$

1. Show that $\displaystyle {s_n}$ is an increasing sequence.

2. show that $\displaystyle {s_n}$ is bounded from above

3.Compute $\displaystyle \lim_{n\rightarrow \infty} $ of $\displaystyle s_n$