Chapter 9, Problem 12RE

Suppose that the sequence $\left\{ak\right\}$ is defined recursively by

$a_o=c,a_{k+1}=\sqrt{a_k}$

Assuming that the sequence converges, find its limit if

$\begin{array}{l}\text{(a)}c=\frac{1}{2}\\ \text{(b)}c=\frac{3}{2}.\end{array}$