Question

Expand the following expression as a series in ascending powers of x up to the terms in x^3. State the range of values of x in each case for which expansion is valid.

Answer 1

(1+x+x^2)^-1

Answer 2

@mathmate

Answer 3

Do you know how to expand 1/(1+x)?

Answer 4

1(1+x)^-1

Answer 5

yes, but expand into a series using Taylor's expansion.
The result should be 1-x+x^2-x^3....

Answer 6

Is Taylor expansion same as binomial series

Answer 7

Not exactly.

Answer 8

Or MacLaurin's series expansion, perhaps?
Taylor's series is an expansion of a function into a power series about any point.
MacLaurin's series expands also into a power series, but about 0.

Answer 9

Here's a link to Mathworld for Maclaurin series. See if it is familiar to you.

Answer 10

Another option is to just do the long division :) lol
It's pretty inefficient but fun if you just want to generate the first few terms.

Answer 11

Do you know hw to solve it using binomial expansion.. like this