Calculus II · Unit 4A · quiz

Unit 4A Concept Quiz

• True or false: if $a_n\to0$ , then $\sum a_n$ converges. • What sequence determines whether $\sum a_n$ converges? • State the geometric convergence condition. • What does absolute convergence guarantee? • When is the Ratio Test inconclusive? • What quantity bounds alternating-series error?

After the explanation

Use the section idea

Reading lens

Mixed work removes the method label; classify first, complete an honest attempt, then diagnose the earliest incorrect decision.

Mental model

A complete series argument includes hypotheses, a named theorem or comparison, its conclusion, and any requested sum or error estimate.

Decision

Identify the object and structure before computing, then use answer reveals only after recording a complete justification.

Common trap

Reading the key before choosing a test or treating a missing hypothesis as a minor presentation issue.

Check yourself

Can you reproduce the argument without the key and explain why a tempting alternative test is weaker?

Structured concept quiz

Unit 4A Concept Quiz

Write a response before revealing the model. These conceptual items use an honest attempt-and-reveal rubric rather than pretending an open response has one machine-provable wording.

Interactive checkunit-4a-concept-quiz-q01

True or false: if $a_n\to0$ , then $\sum a_n$ converges.