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

The answer to taylor (1+x)^{-5} is 1-5x+15x^2-35x^3+70x^4+\ldots

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taylor (1+x)^{-5}

taylor

(1 + x)^{- 5}

1 - 5 x + 15 x^{2} - 35 x^{3} + 70 x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 5}{1 !} x + \frac{30}{2 !} x^{2} + \frac{- 210}{3 !} x^{3} + \frac{1680}{4 !} x^{4} + \dots

Refine

= 1 - 5 x + 15 x^{2} - 35 x^{3} + 70 x^{4} + \dots

\frac{\partial}{\partial y} (\frac{1}{y} e^{x y})

\int_{1}^{13} \frac{x - 1}{72} d x

(- 1, 1), (1, 0)

\frac{d}{d x} (\frac{2}{cos ( 7 x )})

f (x) = x^{4}

What is taylor (1+x)^{-5} ?
The answer to taylor (1+x)^{-5} is 1-5x+15x^2-35x^3+70x^4+\ldots