What is maclaurin ln(1-2x) ?

The answer to maclaurin ln(1-2x) is -2x-2x^2-8/3 x^3-4x^4-32/5 x^5+\ldots

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maclaurin ln(1-2x)

maclaurin

ln (1 - 2 x)

- 2 x - 2 x^{2} - \frac{8}{3} x^{3} - 4 x^{4} - \frac{32}{5} x^{5} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{- 2}{1 !} x + \frac{- 4}{2 !} x^{2} + \frac{- 16}{3 !} x^{3} + \frac{- 96}{4 !} x^{4} + \frac{- 768}{5 !} x^{5} + \dots

Refine

= - 2 x - 2 x^{2} - \frac{8}{3} x^{3} - 4 x^{4} - \frac{32}{5} x^{5} + \dots

\int (2 x + 4)^{3} d x

\frac{\partial}{\partial y} (x^{6 y})

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 1, y^{^{'}} (0) = k

(1 + \frac{3}{y} + x) (\frac{d y}{d x}) + y = \frac{3}{x} - 1

(9, - 10), (- 10, 3)

What is maclaurin ln(1-2x) ?
The answer to maclaurin ln(1-2x) is -2x-2x^2-8/3 x^3-4x^4-32/5 x^5+\ldots