What is maclaurin (1+x)^{-7/3} ?

The answer to maclaurin (1+x)^{-7/3} is 1-7/3 x+35/9 x^2-455/81 x^3+1820/243 x^4+\ldots

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maclaurin (1+x)^{-7/3}

maclaurin

(1 + x)^{- \frac{7}{3}}

1 - \frac{7}{3} x + \frac{35}{9} x^{2} - \frac{455}{81} x^{3} + \frac{1820}{243} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 + x ) ^{- \frac{7}{3}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + x ) ^{- \frac{7}{3}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + x ) ^{- \frac{7}{3}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- \frac{7}{3}}{1 !} x + \frac{\frac{70}{9}}{2 !} x^{2} + \frac{- \frac{910}{27}}{3 !} x^{3} + \frac{\frac{14560}{81}}{4 !} x^{4} + \dots

Refine

= 1 - \frac{7}{3} x + \frac{35}{9} x^{2} - \frac{455}{81} x^{3} + \frac{1820}{243} x^{4} + \dots

x \to 0 lim (3 e^{2 x})

\frac{d}{d x} ((x - 1)^{3})

2 cos^{2} (x)

y = x^{2} + x, (4, 20)

(2 y^{2} + 4 x^{2}) d x = x y d y

What is maclaurin (1+x)^{-7/3} ?
The answer to maclaurin (1+x)^{-7/3} is 1-7/3 x+35/9 x^2-455/81 x^3+1820/243 x^4+\ldots