The Confusing Continued Fraction

I wanted to find the value of the following continued fraction.

\[ {\Large x=\frac{4}{-3+\frac{4}{-3+\frac{4}{-3+\ddots}}}} \]

Now due to the presence of the $-3$ in the denominator, it is not known a priori if the denominator would be positive or negative. Thus, I am not sure if it can be concluded if the result will be positive or negative.

The confusion that I have is about the actual value of $x$ . Is $x=-1$ or $x=4$ ?

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

Its -1 due to the fact that when you put any number except 4 at the bottom of that fraction it approaches -1

Jacob Kirmayer - 2 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$