taylor (2-x)^{-1}

Lösung

taylor

(2 - x)^{- 1}

\frac{1}{2} + \frac{1}{4} x + \frac{1}{8} x^{2} + \frac{1}{16} x^{3} + \frac{1}{32} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{2} + \frac{\frac{1}{4}}{1 !} x + \frac{\frac{1}{4}}{2 !} x^{2} + \frac{\frac{3}{8}}{3 !} x^{3} + \frac{\frac{3}{4}}{4 !} x^{4} + \dots

Fasse zusammen

= \frac{1}{2} + \frac{1}{4} x + \frac{1}{8} x^{2} + \frac{1}{16} x^{3} + \frac{1}{32} x^{4} + \dots

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