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

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

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taylor (1+x)/(1-x)

taylor

\frac{1 + x}{1 - x}

1 + 2 x + 2 x^{2} + 2 x^{3} + 2 x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{2}{1 !} x + \frac{4}{2 !} x^{2} + \frac{12}{3 !} x^{3} + \frac{48}{4 !} x^{4} + \dots

Refine

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

\int_{0}^{e} ln (x) d x

\int (1 + e)^{x} d x

\frac{d y}{d x} = \frac{y ^{3}}{x ^{2}}

\int x^{3} (1 - x^{4})^{5} d x

\int (\frac{7}{1 - x ^{2}}) d x

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