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Popular Calculus >

taylor 1/(x-1)

Solution

taylor

\frac{1}{x - 1}

Solution

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - 1 + \frac{- 1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{- 24}{4 !} x^{4} + \dots

Refine

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

Popular Examples

integral of ln(e^{2x-1})

(\partial)/(\partial x)(2x+2y^2)

taylor xsin(x^3)

derivative of x^{-2/4}+x^{2/4}

integral from 0 to 1 of 1/((x-1)^{2/3)}

Frequently Asked Questions (FAQ)

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