What is taylor x/(2-x) ?

The answer to taylor x/(2-x) is 1/2 x+1/4 x^2+1/8 x^3+1/16 x^4+1/32 x^5+\ldots

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taylor x/(2-x)

taylor

\frac{x}{2 - x}

\frac{1}{2} x + \frac{1}{4} x^{2} + \frac{1}{8} x^{3} + \frac{1}{16} x^{4} + \frac{1}{32} x^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{\frac{1}{2}}{1 !} x + \frac{\frac{1}{2}}{2 !} x^{2} + \frac{\frac{3}{4}}{3 !} x^{3} + \frac{\frac{3}{2}}{4 !} x^{4} + \frac{\frac{15}{4}}{5 !} x^{5} + \dots

Refine

= \frac{1}{2} x + \frac{1}{4} x^{2} + \frac{1}{8} x^{3} + \frac{1}{16} x^{4} + \frac{1}{32} x^{5} + \dots

\frac{\partial}{\partial x} (\frac{x y}{4})

\int x^{3} - 30 x d x

\frac{d}{d x} ((\frac{2 x + 1}{e + 1})^{e})

\frac{\partial}{\partial x} (x ∣ x ∣)

t \to - 1 lim (\frac{e ^{t}}{( \frac{e ^{t} - 6}{5} )})

What is taylor x/(2-x) ?
The answer to taylor x/(2-x) is 1/2 x+1/4 x^2+1/8 x^3+1/16 x^4+1/32 x^5+\ldots