taylor ((1+x/2))/((1-x/2))

Lösung

taylor

\frac{( 1 + \frac{x}{2} )}{( 1 - \frac{x}{2} )}

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

Schritte zur Lösung

Apply the Taylor Formula

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

Evaluate Derivatives

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

Fasse zusammen

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

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