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Popular Calculus >

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

derivative of y=(x^2+6x+2)^3

d er i v a t i v e y = (x^{2} + 6 x + 2)^{3}

integral of 1/(v^2+v)

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

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

d er i v a t i v e f (x) = arctan (x)

(\partial)/(\partial y)(xye^y)

\frac{\partial}{\partial y} (x y e^{y})

integral of sin(22x)cos(15x)

\int sin (22 x) cos (15 x) d 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