taylor 1/(1-x),9

Lösung

taylor

\frac{1}{1 - x}, 9

- \frac{1}{8} + \frac{1}{64} (x - 9) - \frac{1}{512} (x - 9)^{2} + \frac{1}{4096} (x - 9)^{3} - \frac{1}{32768} (x - 9)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= - \frac{1}{8} + \frac{\frac{d}{d x} ( \frac{1}{1 - x} ) ( 9 )}{1 !} (x - 9) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - x} ) ( 9 )}{2 !} (x - 9)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - x} ) ( 9 )}{3 !} (x - 9)^{3} + \dots

Evaluate Derivatives

= - \frac{1}{8} + \frac{\frac{1}{64}}{1 !} (x - 9) + \frac{- \frac{1}{256}}{2 !} (x - 9)^{2} + \frac{\frac{3}{2048}}{3 !} (x - 9)^{3} + \frac{- \frac{3}{4096}}{4 !} (x - 9)^{4} + \dots

Fasse zusammen

= - \frac{1}{8} + \frac{1}{64} (x - 9) - \frac{1}{512} (x - 9)^{2} + \frac{1}{4096} (x - 9)^{3} - \frac{1}{32768} (x - 9)^{4} + \dots