+0

# the 1s and the 2s alternate

0
95
1

What real number is equal to the expression $$2 + \frac{1}{1 + \frac{1}{2 + \frac{1}{1 + \cdots}}}$$, where the 1s and the 2s alternate?

Nov 23, 2020

#1
+31703
+2

Treat this as follows:   $$x = 2+\frac{1}{1+\frac{1}{x}}$$

or   $$x =2+\frac{x}{1+x}$$

Rearrange this to obtain a quadratic equation in x and solve for x (only the positive solution will apply).

Nov 23, 2020