What is taylor 1/((1+4x)) ?

The answer to taylor 1/((1+4x)) is 1-4x+16x^2-64x^3+256x^4+\ldots

Popular >

taylor 1/((1+4x))

taylor

\frac{1}{( 1 + 4 x )}

1 - 4 x + 16 x^{2} - 64 x^{3} + 256 x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( \frac{1}{1 + 4 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 + 4 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 + 4 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 4}{1 !} x + \frac{32}{2 !} x^{2} + \frac{- 384}{3 !} x^{3} + \frac{6144}{4 !} x^{4} + \dots

Refine

= 1 - 4 x + 16 x^{2} - 64 x^{3} + 256 x^{4} + \dots

\frac{\partial}{\partial x} (cos (y^{2}) + y e^{x})

\int \frac{1}{x ^{2} + 6 x + 6} d x

\frac{d y}{d x} + 2 x y = x^{3}

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

\int_{- 2}^{3} \frac{40}{x ^{4}} d x

What is taylor 1/((1+4x)) ?
The answer to taylor 1/((1+4x)) is 1-4x+16x^2-64x^3+256x^4+\ldots