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

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

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taylor 1/((1-x)),2

taylor

\frac{1}{( 1 - x )}, 2

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

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

\int \frac{x ^{2} - 19}{x ^{3} - 2 x ^{2} + x} d x

\int 0.2 x d x

\frac{d x}{d t} = \frac{7 x ^{2} + 3 t 8 t ^{2} + x ^{2}}{7 t x}

\int t \cdot ln (t) d t

y = (4 x^{2} + 5) (3 x - 5)

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