# Maclaurin Series Help

1. Dec 6, 2008

### DjDriftX

Find the first few terms of the Taylor Series around x=0...?
of the function

f(x)= {x/(e^x - 1) , x =/ 0}
{1 , x=0}

the function is piecewise.
up to and including the term involving x^2

It says to not compute derivatives of f but to use the formula for the Taylor series of e^x

x/(e^x-1) = x (1/(e^x-1)
so.
would that be x (1/ $$\sum$$(xn/n!) - 1)
or maybe x $$\sum$$ (1 / (xn/n!) - 1))

I'm not really sure where to start
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 6, 2008

### Dick

Remember you only need terms up to and including x^2. 1-e^x=x+x^2/2!+x^3/3!+... Divide numerator and denominator by x. Now you've got 1/(1+x/2!+x^2/3!+...). You know an expansion for 1/(1+a), right? Use it. Throw away terms that are higher power than you are looking for.