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

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