Calculus II For Dummies
Book image
Explore Book Buy On Amazon

The Sum Rule for integration allows you to split a sum inside an integral into the sum of two separate integrals. Similarly, you can break a sum inside a series into the sum of two separate series:

You can break a sum inside a series into the sum of two separate series

For example:

A series in sigma notation.

A little algebra allows you to split this fraction into two terms:

A fraction series expressed in two terms.

Now the rule allows you to split this result into two series:

Using the sum rule to split an integral into two simplified series.

This sum of two series is equivalent to the series that you started with. As with the Sum Rule for integration, expressing a series as a sum of two simpler series tends to make problem-solving easier. Generally speaking, as you proceed onward with series, any trick you can find to simplify a difficult series is a good thing.

About This Article

This article is from the book:

About the book author:

Mark Zegarelli, a math tutor and writer with 25 years of professional experience, delights in making technical information crystal clear — and fun — for average readers. He is the author of Logic For Dummies and Basic Math & Pre-Algebra For Dummies.

This article can be found in the category: