What is taylor f(x)=(1+x)^{-4} ?

The answer to taylor f(x)=(1+x)^{-4} is 1-4x+10x^2-20x^3+35x^4+\ldots

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taylor f(x)=(1+x)^{-4}

taylor

f (x) = (1 + x)^{- 4}

1 - 4 x + 10 x^{2} - 20 x^{3} + 35 x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 + x ) ^{- 4} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + x ) ^{- 4} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + x ) ^{- 4} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 4}{1 !} x + \frac{20}{2 !} x^{2} + \frac{- 120}{3 !} x^{3} + \frac{840}{4 !} x^{4} + \dots

Refine

= 1 - 4 x + 10 x^{2} - 20 x^{3} + 35 x^{4} + \dots

What is taylor f(x)=(1+x)^{-4} ?
The answer to taylor f(x)=(1+x)^{-4} is 1-4x+10x^2-20x^3+35x^4+\ldots