taylor 1/(x-1),25

Lösung

taylor

\frac{1}{x - 1}, 25

\frac{1}{24} - \frac{1}{576} (x - 25) + \frac{1}{13824} (x - 25)^{2} - \frac{1}{331776} (x - 25)^{3} + \frac{1}{7962624} (x - 25)^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= \frac{1}{24} + \frac{\frac{d}{d x} ( \frac{1}{x - 1} ) ( 25 )}{1 !} (x - 25) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{x - 1} ) ( 25 )}{2 !} (x - 25)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{x - 1} ) ( 25 )}{3 !} (x - 25)^{3} + \dots

Evaluate Derivatives

= \frac{1}{24} + \frac{- \frac{1}{576}}{1 !} (x - 25) + \frac{\frac{1}{6912}}{2 !} (x - 25)^{2} + \frac{- \frac{1}{55296}}{3 !} (x - 25)^{3} + \frac{\frac{1}{331776}}{4 !} (x - 25)^{4} + \dots

Fasse zusammen

= \frac{1}{24} - \frac{1}{576} (x - 25) + \frac{1}{13824} (x - 25)^{2} - \frac{1}{331776} (x - 25)^{3} + \frac{1}{7962624} (x - 25)^{4} + \dots

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