What is taylor g(x)= 1/((1+2x)^3) ?

The answer to taylor g(x)= 1/((1+2x)^3) is 1-6x+24x^2-80x^3+240x^4+\ldots

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taylor g(x)= 1/((1+2x)^3)

taylor

g (x) = \frac{1}{( 1 + 2 x ) ^{3}}

1 - 6 x + 24 x^{2} - 80 x^{3} + 240 x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 6}{1 !} x + \frac{48}{2 !} x^{2} + \frac{- 480}{3 !} x^{3} + \frac{5760}{4 !} x^{4} + \dots

Refine

= 1 - 6 x + 24 x^{2} - 80 x^{3} + 240 x^{4} + \dots

1 - cos (x)

\int_{- π}^{π} π sin^{2} (x) d x

n = 1 \sum \infty \frac{( ( - 2 ) ^{n - 1} )}{7 ^{n}}

\int_{0}^{1} \frac{- 4 y}{e ^{2 y}} d y

\frac{\partial}{\partial x} (6 x^{2} y + 9 x y^{3})

What is taylor g(x)= 1/((1+2x)^3) ?
The answer to taylor g(x)= 1/((1+2x)^3) is 1-6x+24x^2-80x^3+240x^4+\ldots