# Taylor series

#### VBDX

##### New member
Hi!

I'm trying to expand this function using Taylor expansion, that is, find a way to represent algebraically the coefficients of the expansion of the following function

$$\displaystyle \frac{2x^4-x^3-x^2-x+1}{1-2x+x^5}$$

I'm trying to do this on the point $$\displaystyle x=0$$, but I really need to know the algebraic form of these coefficients.

Thaks!

#### topsquark

##### Full Member
Hi!

I'm trying to expand this function using Taylor expansion, that is, find a way to represent algebraically the coefficients of the expansion of the following function

$$\displaystyle \frac{2x^4-x^3-x^2-x+1}{1-2x+x^5}$$

I'm trying to do this on the point $$\displaystyle x=0$$, but I really need to know the algebraic form of these coefficients.

Thaks!
Are you using a Taylor expansion or a MacLaurin expansion? In a Taylor expansion we expand in terms of x - a where a is small and for a MacLaurin expansion we expand in terms of x where x is small.

Frankly unless you are told to do this by a Taylor (or MacLaurin) expansion I'd avoid it. The derivatives are going to be pretty messy. (And note that x = 1 gives an indeterminate value.) I'd do the long division, then do the expansion.

-Dan

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi!

I'm trying to expand this function using Taylor expansion, that is, find a way to represent algebraically the coefficients of the expansion of the following function

$$\displaystyle \frac{2x^4-x^3-x^2-x+1}{1-2x+x^5}$$

I'm trying to do this on the point $$\displaystyle x=0$$, but I really need to know the algebraic form of these coefficients.

Thaks!
Did you calculate f(0), f'(0), f"(0),.... etc.?