# Taylor series strategy

I am trying to find the maclaurin series for f(x) = (1 + x)^(-3)

--> what is the best way of doing this--to make a table and look for a trend in f^(n)?

## Answers and Replies

rock.freak667
Homework Helper
.....well you can do that but you will just find that is just a binomial series.

do you know the nth term in a binomial expansion?

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morphism
Science Advisor
Homework Helper
Presumably you know the expansion of 1/(1+x) (hint: think geometric series). So what's the second derivative of 1/(1+x), and how does this help? This should give you another way of finding the expansion of (1+x)^(-3).

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NO!!! NO!! NO!! there should be no binomals involved. Is there a simpler way? the way we usually do this is by making a table.

If someone can shed some light, I would appreciate it.

rock.freak667
Homework Helper
Well you will have to find f(0),f'(0),f'''(0) and so forth for the traditional method for finding the maclaurin series for that function. But I believe that you should make the table and then make the series if that is the way you know how to do it

morphism
Science Advisor
Homework Helper
NO!!! NO!! NO!! there should be no binomals involved. Is there a simpler way? the way we usually do this is by making a table.

If someone can shed some light, I would appreciate it.
Read my post...

HallsofIvy
Science Advisor
Homework Helper
NO!!! NO!! NO!! there should be no binomals involved. Is there a simpler way? the way we usually do this is by making a table.

If someone can shed some light, I would appreciate it.

You can, in fact, extend the binomial theorem to fractional or negative exponents. Morphism suggested an even easier way. You'[ve already been given two very good ways of finding the series. Why don't you appreciate them?