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

The answer to taylor 1/(sqrt(1-x)) is 1+1/2 x+3/8 x^2+5/16 x^3+35/128 x^4+\ldots

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taylor 1/(sqrt(1-x))

taylor

\frac{1}{1 - x}

1 + \frac{1}{2} x + \frac{3}{8} x^{2} + \frac{5}{16} x^{3} + \frac{35}{128} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{1}{2}}{1 !} x + \frac{\frac{3}{4}}{2 !} x^{2} + \frac{\frac{15}{8}}{3 !} x^{3} + \frac{\frac{105}{16}}{4 !} x^{4} + \dots

Refine

= 1 + \frac{1}{2} x + \frac{3}{8} x^{2} + \frac{5}{16} x^{3} + \frac{35}{128} x^{4} + \dots

\frac{d}{d x} (\frac{8 x}{3 - tan ( x )})

f (x) = 7 x + 2

\frac{d y}{d x} = \frac{( x - 3 )}{2 - y}

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

\frac{d}{d x} (sec^{2} (x) tan (x))

What is taylor 1/(sqrt(1-x)) ?
The answer to taylor 1/(sqrt(1-x)) is 1+1/2 x+3/8 x^2+5/16 x^3+35/128 x^4+\ldots