What is maclaurin (1-2x)^{-2} ?

The answer to maclaurin (1-2x)^{-2} is 1+4x+12x^2+32x^3+80x^4+\ldots

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maclaurin (1-2x)^{-2}

maclaurin

(1 - 2 x)^{- 2}

1 + 4 x + 12 x^{2} + 32 x^{3} + 80 x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{4}{1 !} x + \frac{24}{2 !} x^{2} + \frac{192}{3 !} x^{3} + \frac{1920}{4 !} x^{4} + \dots

Refine

= 1 + 4 x + 12 x^{2} + 32 x^{3} + 80 x^{4} + \dots

n = 2 \sum \infty \frac{n}{3 n ^{3} + 1}

\frac{8}{1 - x}

\frac{d}{d t} (4 t^{2} + 2 t + 5)

\frac{d}{d x} (e^{c o s (x)} + e^{s i n (y)})

\frac{d}{d x} (lo g_{3} (5 x - 1))

What is maclaurin (1-2x)^{-2} ?
The answer to maclaurin (1-2x)^{-2} is 1+4x+12x^2+32x^3+80x^4+\ldots