# Are we any closer?

**Algebra**Level 3

A fraction is called continuous fraction, If it is of the form:

\(Y=\large1+\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5+\frac{.}{.+\frac{.}{.}}}}}}\)

knowing the above fraction, what can be said about \(Z\), which contains the continued fraction below:

\(Z=\huge1+\frac{1}{2-\frac{1}{3+\frac{1}{4-\frac{1}{5+\frac{.}{.-\frac{.}{.+\frac{.}{..\frac{.}{.\frac{1}{(n-1)[\pm]\frac{1}{n}}}}}}}}}}\)

where \(n\) is any positive integer, and the \([\pm]\)sign in the last fraction indicates that \(n\) can be either even or odd. It will be a \(+\) if \(n\) is even and a \(-\) if \(n\) is odd.

This problem is a part of the set All-Zebra