What is the comparison test?

Problem Statement

What is the comparison test?

Step-by-Step Explanation

The comparison test determines convergence by comparing a series to another series whose behavior is known.

1. Identify what the question is asking. In Calculus 2, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Final Answer

The comparison test determines convergence by comparing a series to another series whose behavior is known. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.