What is maclaurin (1+x)^{-2/5} ?

The answer to maclaurin (1+x)^{-2/5} is 1-2/5 x+7/25 x^2-28/125 x^3+119/625 x^4+\ldots

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maclaurin (1+x)^{-2/5}

maclaurin

(1 + x)^{- \frac{2}{5}}

1 - \frac{2}{5} x + \frac{7}{25} x^{2} - \frac{28}{125} x^{3} + \frac{119}{625} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{2}{5}}{1 !} x + \frac{\frac{14}{25}}{2 !} x^{2} + \frac{- \frac{168}{125}}{3 !} x^{3} + \frac{\frac{2856}{625}}{4 !} x^{4} + \dots

Refine

= 1 - \frac{2}{5} x + \frac{7}{25} x^{2} - \frac{28}{125} x^{3} + \frac{119}{625} x^{4} + \dots

What is maclaurin (1+x)^{-2/5} ?
The answer to maclaurin (1+x)^{-2/5} is 1-2/5 x+7/25 x^2-28/125 x^3+119/625 x^4+\ldots