Explanation

(b)
Let $x = 2 + \frac{1}{2 + \frac{1}{2 + ...\infty}}$
$\Rightarrow x = 2 + \frac{1}{x}$
$\Rightarrow x^{2} - 2x - 1 = 0$
$\Rightarrow x = \frac{2 \pm \sqrt{4 + 4}}{2}$
$\Rightarrow x = 1 \pm \sqrt{2}$
But the value of the given expression cannot be negative or less than 2, therefore $1 + \sqrt{2}$ is required answer.