What is taylor 1/(2x-1) ?

The answer to taylor 1/(2x-1) is -1-2x-4x^2-8x^3-16x^4+\ldots

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taylor 1/(2x-1)

taylor

\frac{1}{2 x - 1}

- 1 - 2 x - 4 x^{2} - 8 x^{3} - 16 x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= - 1 + \frac{- 2}{1 !} x + \frac{- 8}{2 !} x^{2} + \frac{- 48}{3 !} x^{3} + \frac{- 384}{4 !} x^{4} + \dots

Refine

= - 1 - 2 x - 4 x^{2} - 8 x^{3} - 16 x^{4} + \dots

f^{^{'}} (x) = - 2

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

\int (\frac{1}{1 - 2 x} - cos (\frac{x}{3})) d x

\int sin^{5} (4 x) d x

x \to 9 lim (\frac{1}{x ^{2}})

What is taylor 1/(2x-1) ?
The answer to taylor 1/(2x-1) is -1-2x-4x^2-8x^3-16x^4+\ldots