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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
10 months, 4 weeks ago

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