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Calculus/Maclaurin Series

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Expert: - 10/26/2008


Question
What would be the Maclaurin series for (1-cosx)/(x^2),(x≠0) and what would be the easiest way to finding that answer.

Answer
A Maclaurin Series is a Taylor's Series with the expansion being about 0.
It is given in the top of
//mathworld.wolfram.com/MaclaurinSeries.html
.

It seems to me the only way to find an answer is to differentiate the function that you've got several times until a pattern is seen.
I don't see on at the moment, except that the bottom always has a
x^(2n) for the nth term.  The top starts to look difficult very soon.

After only one derivative, you get (x^2sin(x) - 2x + 2xcos(x)/x^4.
After each one, they get more complicated.
Take several derivatives and see if there is a patter of what is multiplied by sin(x), cos(x), and by itself.

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