What is maclaurin (1+x)^{-2/3} ?

The answer to maclaurin (1+x)^{-2/3} is 1-2/3 x+5/9 x^2-40/81 x^3+110/243 x^4+\ldots

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maclaurin (1+x)^{-2/3}

maclaurin

(1 + x)^{- \frac{2}{3}}

1 - \frac{2}{3} x + \frac{5}{9} x^{2} - \frac{40}{81} x^{3} + \frac{110}{243} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{- \frac{2}{3}}{1 !} x + \frac{\frac{10}{9}}{2 !} x^{2} + \frac{- \frac{80}{27}}{3 !} x^{3} + \frac{\frac{880}{81}}{4 !} x^{4} + \dots

Refine

= 1 - \frac{2}{3} x + \frac{5}{9} x^{2} - \frac{40}{81} x^{3} + \frac{110}{243} x^{4} + \dots

y = (1 + 2 x)^{10}, (0, 1)

5 x arcsin (x)

\int \frac{1 - 2 y}{y ^{2}} d y

\frac{d}{d x} (e^{x + y} - x)

\frac{d}{d x} (cos (sin (6 x)))

What is maclaurin (1+x)^{-2/3} ?
The answer to maclaurin (1+x)^{-2/3} is 1-2/3 x+5/9 x^2-40/81 x^3+110/243 x^4+\ldots