1-1-1-2-1-2-3-2-1-3-4-3-1-4-5-4-1-5-6-5-

Question Number 127644 by Dwaipayan Shikari last updated on 31/Dec/20

\frac{1}{1 - \frac{1}{2 - \frac{\frac{1}{2}}{\frac{3}{2} - \frac{\frac{1}{3}}{\frac{4}{3} - \frac{\frac{1}{4}}{\frac{5}{4} - \frac{\frac{1}{5}}{\frac{6}{5} - \dots}}}}}}

Commented by Dwaipayan Shikari last updated on 31/Dec/20

a_{0} + a_{0} a_{1} + a_{0} a_{2} a_{1} + a_{0} a_{1} a_{2} a_{3} + \dots . . = \frac{a_{0}}{1 - \frac{a_{1}}{1 + a_{1} - \frac{a_{2}}{1 + a_{2} - \frac{a_{3}}{1 + a_{3} - \frac{a_{4}}{1 + a_{4} . .}}}}}

e^{x} = 1 + x + \frac{x^{2}}{2} + \frac{x^{3}}{6} + \dots

= 1 + 1 . x + x (\frac{x}{2}) + x (\frac{x}{2}) (\frac{x}{3}) + x . \frac{x}{2} . \frac{x}{3} . \frac{x}{4} + . .

= \frac{1}{1 - \frac{x}{1 + x - \frac{\frac{x}{2}}{1 + \frac{x}{2} - \frac{\frac{x}{3}}{1 + \frac{x}{3} - \frac{\frac{x}{4}}{1 + \frac{x}{4} - . .}}}}}

e = \frac{1}{1 - \frac{1}{2 - \frac{\frac{1}{2}}{\frac{3}{2} - \frac{\frac{1}{3}}{\frac{4}{3} - \frac{\frac{1}{4}}{\frac{5}{4} . .}}}}}

Commented by MathSh last updated on 31/Dec/20

e

Facebook Tweet Pin