Section 10.12

Strategy for Series

With so many tests available, how do you choose the right one?

1

Introduction

Determining series convergence is often about pattern recognition. Does it look geometric? Does it have factorials? Is it rational?

There is no single "correct" order, but following a systematic approach can save you from dead ends.

2

Interactive Strategy Tool

Series Convergence Decision Tree

Does the limit of terms approach 0?

Calculate lim(an) as n approaches infinity.

Click through to see which test applies to your problem!

3

General Guidelines

1. Divergence Test

Check first. If it's not 0, you're done! (It diverges).

2. Special Forms

  • Geometric: .
  • p-Series: .

3. Comparisons

If it looks almost like a p-series or geometric series (e.g. rational functions), use Comparison or Limit Comparison.

4. Alternating

If it has , use the Alternating Series Test.

5. Factorials / Powers

Involving or ? Use the Ratio Test.
If everything is raised to the nth wpower , use the Root Test.

6. Integral Test

If is easily integrable, positive, and decreasing.

4

Practice Quiz

Loading...