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

The answer to taylor 1/(1-x^2),0 is 1+x^2+x^4+x^6+x^8+\ldots

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taylor 1/(1-x^2),0

taylor

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

1 + x^{2} + x^{4} + x^{6} + x^{8} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{40320}{8 !} x^{8} + \dots

Refine

= 1 + x^{2} + x^{4} + x^{6} + x^{8} + \dots

\frac{d}{d x} (- \frac{x}{5})

x \to 2 lim (3 x^{3} - 5 x)

\int_{100}^{120} \frac{600}{x} d x

f (x) = 4 x^{2} - x^{3}, at x = 1

\frac{d y}{d x} + 2 y = 3

What is taylor 1/(1-x^2),0 ?
The answer to taylor 1/(1-x^2),0 is 1+x^2+x^4+x^6+x^8+\ldots