taylor 1/(1-1/x),0

Lösung

taylor

\frac{1}{1 - \frac{1}{x}}, 0

- x - x^{2} - x^{3} - x^{4} - x^{5} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( \frac{1}{1 - \frac{1}{x}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - \frac{1}{x}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - \frac{1}{x}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{- 1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{- 24}{4 !} x^{4} + \frac{- 120}{5 !} x^{5} + \dots

Fasse zusammen

= - x - x^{2} - x^{3} - x^{4} - x^{5} + \dots