### Home > APCALC > Chapter 9 > Lesson 9.2.2 > Problem9-71

9-71.

A variant of Ying’s method (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 $S$.

$S^2=2S+1$

$S^2-2S-1=0$

Use the Quadratic Formula to solve for $S$.