taylor (1+x)^{-3/5}

Lösung

taylor

(1 + x)^{- \frac{3}{5}}

1 - \frac{3}{5} x + \frac{12}{25} x^{2} - \frac{52}{125} x^{3} + \frac{234}{625} x^{4} + \dots

Schritte zur Lösung

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 + x ) ^{- \frac{3}{5}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + x ) ^{- \frac{3}{5}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + x ) ^{- \frac{3}{5}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- \frac{3}{5}}{1 !} x + \frac{\frac{24}{25}}{2 !} x^{2} + \frac{- \frac{312}{125}}{3 !} x^{3} + \frac{\frac{5616}{625}}{4 !} x^{4} + \dots

Fasse zusammen

= 1 - \frac{3}{5} x + \frac{12}{25} x^{2} - \frac{52}{125} x^{3} + \frac{234}{625} x^{4} + \dots

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