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# 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 $$x=4$$?

Note by Janardhanan Sivaramakrishnan
7 months ago