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Popular >

taylor (1-x)^{-1}

Solution

taylor

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

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y = (x^{2} + 6 x + 2)^{3}

integral from-2 to 1 of 2\sqrt[3]{2-3x}

integral of 1/(v^2+v)

\int \frac{1}{v ^{2} + v} d v

derivative of (5x-2)^2(4-x^3)^2 derivative of

(5 x - 2)^{2} (4 - x^{3})^{2}

derivative of f(x)=arctan(sqrt(x))derivative of

f (x) = arctan (x)

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