Chapter 9.1, Problem 86E

Using a Sequence Consider the sequence $\left\{a_n\right\}$, where $a_1=\sqrt{k,}{a}_{n-1}=\sqrt{k+a_n}$, and $k>0$

(a) Show that $\left\{a_n\right\}$ is increasing and bounded.

(b) Prove that $\underset{n\to \infty }{\lim }{a}_n$ exists.

(c) Find $\underset{n\to \infty }{\lim }{a}_n$