i am using formula no.1 to make a new formula no.5
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3rd formula
1+\cfrac{n+1}{2+\cfrac{n+2}{3+\cfrac{n+3}{4+\cfrac{n+4}{…}}}}=\frac{\frac{d^n}{dx^n}\left ( xe^\frac{x}{1-x} \right )}{\frac{d^{n-1}}{dx^{n-1}}\left ( \frac{x}{1-x}e^\frac{x}{1-x} \right )} at point x = 0 and n > 1
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follow up to yesterday
I am also adding a follow up …
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Generalization for specific type of continued fraction
i used Euler’s continued fraction formula. it helped me solve this. https://en.wikipedia.org/wiki/Eulers_continued_fraction_formula
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