Solve Maclaurin Series for f(x)= 1/(1+x+X2)

[Crazy Gnome]

Homework Statement

Find the Maclaurin series for f(x)= 1/ (1+x+X²)

Homework Equations

The Attempt at a Solution

I think the book says I can just divide 1 by the Maclaurin series of (1+x+X²). And when i do this the original function is the answer (which makes sense).

But when I do it my finding the derivatives of f(x) and then using the formula I get f(x) = 1-x+x³.

So I was wondering if
1) Which way is correct
2) is the second one accurate.

Thanks
-James

 

[Dick]

The second way is accurate. The first way would be as well if you do what they want you to. You are supposed to divide 1 by 1+x+x^2 using polynomial division. The result is NOT 1+x+x^2.