1
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
Using algorithms to discover new mathematics
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