Using the Mean Value Theorem for Integrals
Determining Whether a Taylor Series Is Convergent or Divergent
Determine Signed Areas in a Problem

Using the Sum Rule for Simplifying a Series

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:

image0.png

For example:

image1.png

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

image2.png

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

image3.png

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.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Connecting a Series with Its Two Related Sequences
Find the Area Between Two Functions
Calculating Error Bounds for Taylor Polynomials
Determine Unsigned Area between Curves
How to Split One Definite Integral into Two Definite Integrals
Advertisement

Inside Dummies.com