Answer
(a) $2$.
(b) $L=2$ see explanations.
Work Step by Step
(a) The first ten terms of this sequence rounded to eight decimal places are listed in the table.
This sequence appear to be convergent, and we can guess the value of the limit as $2$.
(b) Given the sequence is convergent to a limit $L$ and
$$\lim_{n\to\infty}a_n=L$$
Let $m=n+1$, we have $m\to\infty$ when $n\to\infty$ thus
$$\lim_{m\to\infty}a_m=L$$
This means that $L=\sqrt {2+L}$ and $L^2=2+L$ or $L^2-L-2=0$ which gives $L=-1, 2$. Discard $-1$ as we know $L$ is positive, so we get the result as $L=2$
