Chapter 9.1, Problem 83E

(a)

To determine

To calculate: The first five terms of the sequence given as, $\sqrt{2},\sqrt{2+\sqrt{2}},\sqrt{2+\sqrt{2+\sqrt{2}}},\dots$.

(b)

To determine

To calculate: The recursion formula for $a_n$ for $n\ge 2$ if the sequence is given as,

$\sqrt{2},\sqrt{2+\sqrt{2}},\sqrt{2+\sqrt{2+\sqrt{2}}},\dots$.

(c)

To determine

To calculate: The value of $\underset{n\to \infty }{\lim }{a}_n$ if the sequence is given as $\sqrt{2},\sqrt{2+\sqrt{2}},\sqrt{2+\sqrt{2+\sqrt{2}}},\dots$.