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

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

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

taylor

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

1 + x + \frac{1}{2} x^{2} + \frac{1}{2} x^{3} + \frac{3}{8} 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{1}{1 !} x + \frac{1}{2 !} x^{2} + \frac{3}{3 !} x^{3} + \frac{9}{4 !} x^{4} + \dots

Refine

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

\int_{0}^{3} π (2 x)^{2} d x

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

\int \frac{x + 1}{x ^{2} + 2 x + 2} d x

\int \frac{x ^{2} - 4}{x ^{3} - 2 x ^{2} + x} d x

\frac{d}{d x} (2^{x s i n (x)})

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