Are we any closer?

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.

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This problem is a part of the set All-Zebra