[ [Systems of linear equations]

Solve the equation $1+1:(1+1:(1+1:(x+2016)))=(1.2)^{2}$.

#
Let's write the left side of the equation as a "multi-story" common fraction and transform it:

$$
\begin{aligned}
& 1+\frac{1}{1+\frac{1}{1+\frac{1}{x+2016}}}=(1.2)^{2} \Leftrightarrow \frac{1}{1+\frac{1}{1+\frac{1}{x+2016}}}=\frac{11}{25} \Leftrightarrow 1+\frac{1}{1+\frac{1}{x+2016}}=\frac{25}{11} \Leftrightarrow \frac{1}{1+\frac{1}{x+2016}}=\frac{14}{11} \Leftrightarrow \\
& 1+\frac{1}{x+2016}=\frac{11}{14} \Leftrightarrow \\
& \Leftrightarrow \frac{1}{x+2016}=-\frac{3}{14} \Leftrightarrow x+2016=-\frac{14}{3} \Leftrightarrow x=-2020^{2} / 3
\end{aligned}
$$

## Answer

$x=-2020^{2} / 3$.

## Problem