What is taylor 1/(2-x),0 ?

The answer to taylor 1/(2-x),0 is 1/2+1/4 x+1/8 x^2+1/16 x^3+1/32 x^4+\ldots

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taylor 1/(2-x),0

taylor

\frac{1}{2 - x}, 0

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{2} + \frac{\frac{1}{4}}{1 !} x + \frac{\frac{1}{4}}{2 !} x^{2} + \frac{\frac{3}{8}}{3 !} x^{3} + \frac{\frac{3}{4}}{4 !} x^{4} + \dots

Refine

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

\frac{d}{d x} (\frac{4 x ^{2}}{x ^{2} - 1})

x^{3} + 7 x - 6

3 x

\int \frac{1}{z ^{2} - 1} d z

f (x) = (6 x^{2} - 10 x) e^{x}

What is taylor 1/(2-x),0 ?
The answer to taylor 1/(2-x),0 is 1/2+1/4 x+1/8 x^2+1/16 x^3+1/32 x^4+\ldots