A variant of Ying's trick (manipulating an infinite expression so that the expression appears as a part of itself) can be used in other situations. For example, it can be used to evaluate an infinite "continued fraction" such as:

$S = 2 + \frac { 1 } { 2 + \frac { 1 } { 2 + \frac { 1 } { 2 + \ldots } } }$

Explain why $S = 2 + \frac { 1 } { S }$ Then solve for $S$.