Use known Maclaurin expansions to find the Maclaurin expansion, by adding, composing, differentiating, and so on.

1/((1-x)^3)

is the function I'm supposed to expand and I don't even know where to start. Thanks in advance!!!!

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- Jul 16th 2007, 03:03 PMTreeMoneyMaclaurin expansion
Use known Maclaurin expansions to find the Maclaurin expansion, by adding, composing, differentiating, and so on.

1/((1-x)^3)

is the function I'm supposed to expand and I don't even know where to start. Thanks in advance!!!! - Jul 16th 2007, 05:36 PMgalactus
MacLaurin expansion is $\displaystyle f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)x^ {3}}{3!}+.......+\frac{f^{n}(0)}{n!}x^{n}$

$\displaystyle f(x)=\frac{1}{(1-x)^{3}}$

$\displaystyle f'(x)=\frac{3}{(x-1)^{4}}$

$\displaystyle f''(x)=\frac{-12}{(x-1)^{5}}$

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$\displaystyle f(0)=1$

$\displaystyle f'(0)x=3x$

$\displaystyle \frac{f''(0)}{2!}x^{2}=6x^{2}$

$\displaystyle \frac{f'''(0)}{3!}x^{3}=10x^{3}$

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See the pattern. - Jul 16th 2007, 06:08 PMTreeMoney
Thanks!!!!!

I wasn't using the derivative correctly. Thanks again!!!

Repped - Jul 16th 2007, 07:53 PMcurvature