Discovering Maclaurin Series for (1 + x)^(-3) with a Taylor Series Approach

[frasifrasi]

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)?

 

[rock.freak667]

...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?

 

[morphism]

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).

 

[frasifrasi]

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]

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]

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]

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?