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

\frac{d}{d x} (\frac{3}{4} x)

\frac{\partial}{\partial y} (\frac{x}{z} + \frac{y}{z})

\frac{s}{( s + 2 )}

y^{^{'}} = \frac{y}{x}, y (2) = 2

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