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

The answer to taylor 2/(1-2x) is 2+4x+8x^2+16x^3+32x^4+\ldots

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taylor 2/(1-2x)

taylor

\frac{2}{1 - 2 x}

2 + 4 x + 8 x^{2} + 16 x^{3} + 32 x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 2 + \frac{4}{1 !} x + \frac{16}{2 !} x^{2} + \frac{96}{3 !} x^{3} + \frac{768}{4 !} x^{4} + \dots

Refine

= 2 + 4 x + 8 x^{2} + 16 x^{3} + 32 x^{4} + \dots

x \to 4 lim (\frac{x - 5}{x + 1})

\frac{\partial}{\partial x} ((2 x - 1)^{3})

9 y^{^{''}} + 6 y = 0

\int \frac{- cos ( 2 x ) - 1}{4} d x

\int \frac{3}{98} x^{2} d x

What is taylor 2/(1-2x) ?
The answer to taylor 2/(1-2x) is 2+4x+8x^2+16x^3+32x^4+\ldots