# Quick question about Taylor Polymonials

• Apr 16th 2013, 01:02 PM
Educated
Quick question:

When they ask for the 'fifth' term of a particular taylor polymonial, which term are they asking for?

Eg. If I had the McLauren series for $e^x = 1 + \dfrac{x}{1!} + \dfrac{x^2}{2!} + \dfrac{x^3}{3!} + \dfrac{x^4}{4!} + \dfrac{x^5}{5!} + \dfrac{x^6}{6!} + ...$

Do they mean the fifth one $\dfrac{x^4}{4!}$ or do they mean the x^5 term?
• Apr 16th 2013, 01:19 PM
HallsofIvy
Re: Quick question about Taylor Polymonials
Since the polynomial starts with $x^0$, the fifth term is $x^4$.
• Apr 16th 2013, 05:02 PM
Educated
Re: Quick question about Taylor Polymonials
What if the Taylor polynomial has zero coefficient terms in it? Eg.

$1 - \dfrac{x^2}{2!} + \dfrac{x^4}{4!} - \dfrac{x^6}{6!} + ...$

Would the third term be $\dfrac{x^4}{4!}$