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

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

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taylor 1/(1+2x)

taylor

\frac{1}{1 + 2 x}

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

x \to 3 lim ((x - 0) \cdot (x - 3))

sin (x), \frac{π}{6}

\int (e^{y^{3} + 2}) d y

(1, 4), (3, - 1)

\int_{0}^{4} (x) d x

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