How should I expand 1/(1+x)^n around x=0?

1. Apr 19, 2013

liyz06

1. The problem statement, all variables and given/known data

How should I expand 1/(1+x)^n around x=0?

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: Apr 19, 2013
2. Apr 19, 2013

Staff: Mentor

Did you try a Taylor expansion?
What did you get? Where did you run into problems?

3. Apr 19, 2013

liyz06

I know that (1+x)^n could be expanded easily by binomial theorem, but what I need here is to expand (1+x)^-n into polynomial form, not the reciprocal of a polynomial

4. Apr 19, 2013

Staff: Mentor

You can just calculate the Taylor expansion.

5. Apr 19, 2013

SammyS

Staff Emeritus
Are you familiar with Taylor Series ?

The Taylor expansion for a function, f(x), expanded about x = a is:

$\displaystyle f(x)=f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots \ .$

So, expanding about x = 0 gives:

$\displaystyle f(x)=f(0)+\frac {f'(0)}{1!} (x)+ \frac{f''(0)}{2!} (x)^2+\frac{f^{(3)}(0)}{3!}(x)^3+ \cdots \ .$