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

The answer to taylor 1/(1-x-x^2),0 is 1+x+2x^2+3x^3+5x^4+\ldots

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

taylor

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

1 + x + 2 x^{2} + 3 x^{3} + 5 x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} x + \frac{4}{2 !} x^{2} + \frac{18}{3 !} x^{3} + \frac{120}{4 !} x^{4} + \dots

Refine

= 1 + x + 2 x^{2} + 3 x^{3} + 5 x^{4} + \dots

n = 0 \sum \infty 4546644

x \to 3 lim ((x^{x} + x)^{x})

(ln (\frac{x}{3}))^{^{'}}

x^{3} (x - 7)^{2}

y = x^{2} + 3

What is taylor 1/(1-x-x^2),0 ?
The answer to taylor 1/(1-x-x^2),0 is 1+x+2x^2+3x^3+5x^4+\ldots