What is taylor (1-x)^{1/5} ?

The answer to taylor (1-x)^{1/5} is 1-1/5 x-2/25 x^2-6/125 x^3-21/625 x^4+\ldots

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

taylor

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

1 - \frac{1}{5} x - \frac{2}{25} x^{2} - \frac{6}{125} x^{3} - \frac{21}{625} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{1}{5}}{1 !} x + \frac{- \frac{4}{25}}{2 !} x^{2} + \frac{- \frac{36}{125}}{3 !} x^{3} + \frac{- \frac{504}{625}}{4 !} x^{4} + \dots

Refine

= 1 - \frac{1}{5} x - \frac{2}{25} x^{2} - \frac{6}{125} x^{3} - \frac{21}{625} x^{4} + \dots

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What is taylor (1-x)^{1/5} ?
The answer to taylor (1-x)^{1/5} is 1-1/5 x-2/25 x^2-6/125 x^3-21/625 x^4+\ldots