# 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

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