What is maclaurin (x^2)/((1+2x)^3) ?

The answer to maclaurin (x^2)/((1+2x)^3) is x^2-6x^3+24x^4-80x^5+240x^6+\ldots

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maclaurin (x^2)/((1+2x)^3)

maclaurin

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

x^{2} - 6 x^{3} + 24 x^{4} - 80 x^{5} + 240 x^{6} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 0 + \frac{0}{1 !} x + \frac{2}{2 !} x^{2} + \frac{- 36}{3 !} x^{3} + \frac{576}{4 !} x^{4} + \frac{- 9600}{5 !} x^{5} + \frac{172800}{6 !} x^{6} + \dots

Refine

= x^{2} - 6 x^{3} + 24 x^{4} - 80 x^{5} + 240 x^{6} + \dots

\int - sin (2 t) d t

\int_{1}^{4} 8 t ln (t) d t

y^{^{'}} = - 0.02 (y - 20)

n = 1 \sum \infty 2 - \frac{5}{2 ^{n}}

\frac{4 x - 1}{2 x + 3}

What is maclaurin (x^2)/((1+2x)^3) ?
The answer to maclaurin (x^2)/((1+2x)^3) is x^2-6x^3+24x^4-80x^5+240x^6+\ldots