# Maclaurin expansion

• July 16th 2007, 03:03 PM
TreeMoney
Maclaurin 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!!!!
• July 16th 2007, 05:36 PM
galactus
MacLaurin expansion is $f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)x^ {3}}{3!}+.......+\frac{f^{n}(0)}{n!}x^{n}$

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

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

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

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$f(0)=1$

$f'(0)x=3x$

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

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

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See the pattern.
• July 16th 2007, 06:08 PM
TreeMoney
Thanks!!!!!

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

Repped
• July 16th 2007, 07:53 PM
curvature
Quote:

Originally Posted by TreeMoney
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!!!!

Use the fact below and a known Maclaurin expansion: