# Thread: help with the taylor series for a bonus problem

1. ## help with the taylor series for a bonus problem

hey all,

i am stuck on a math problem that no one i've talked to can figure out. the idea is i have to find a taylor series in x - a through the term (x - a)^3 for the problem:

2 - x + 3(x^2) - x^3 , a = -1

if anyone has ANY idea at all how this is done, please let me know. thank you.

2. Originally Posted by thatguyinthesuit
hey all,

i am stuck on a math problem that no one i've talked to can figure out. the idea is i have to find a taylor series in x - a through the term (x - a)^3 for the problem:

2 - x + 3(x^2) - x^3 , a = -1

if anyone has ANY idea at all how this is done, please let me know. thank you.
put $\displaystyle u=x-a$, then $\displaystyle x=u+a$ now substutute this into your expression to get:

$\displaystyle 2 + (u+a) + 3(u+a)^2 -(u+a)^3$

now expand the powers and collect terms to give a cubic in $\displaystyle u$ and finaly replace $\displaystyle u$ by $\displaystyle x-a$

RonL