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

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

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taylor 1/(1+2x),0

taylor

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

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

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} x + \frac{8}{2 !} x^{2} + \frac{- 48}{3 !} x^{3} + \frac{384}{4 !} x^{4} + \dots

Refine

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

\frac{d}{d x} ((ln (x)) (\frac{x ^{7} + 3}{x ^{3} - 10}))

\int (3 x - 7)^{9} d x

\int \frac{1}{4 x ^{2} - 9} d x

\frac{d}{d x} (3 sin (x) cos (x))

f (x) = x^{- 1} - \frac{1}{x}

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