What is taylor 1/(x^3) ?

The answer to taylor 1/(x^3) is 1-3(x-1)+6(x-1)^2-10(x-1)^3+15(x-1)^4+\ldots

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taylor 1/(x^3)

taylor

\frac{1}{x ^{3}}

1 - 3 (x - 1) + 6 (x - 1)^{2} - 10 (x - 1)^{3} + 15 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 3}{1 !} (x - 1) + \frac{12}{2 !} (x - 1)^{2} + \frac{- 60}{3 !} (x - 1)^{3} + \frac{360}{4 !} (x - 1)^{4} + \dots

Refine

= 1 - 3 (x - 1) + 6 (x - 1)^{2} - 10 (x - 1)^{3} + 15 (x - 1)^{4} + \dots

\frac{d}{d t} (cos (t) - sin (t))

\int + \frac{e ^{2 x}}{1 + e ^{2 x}} d x

f (x) = 4 x^{2} - 4 x + 1, at x = 1

\frac{\partial}{\partial x} (x sin (x + y) - cos (x + y))

y^{^{'}} = y^{4} \cdot (4 x^{2} + x)

What is taylor 1/(x^3) ?
The answer to taylor 1/(x^3) is 1-3(x-1)+6(x-1)^2-10(x-1)^3+15(x-1)^4+\ldots