Calculus II · Unit 4A · answer key

Unit 4A Practice Exam A Answer Key

Finish an honest attempt first. Then compare one numbered response at a time, locate the first line where your reasoning diverged, and retry without the key open.

Answer 1

Problem 1

$2$ .

Answer 2

Problem 2

Yes, it converges to $0$ .

Answer 3

Problem 3

$5/(1-1/4)=20/3$ .

Answer 4

Problem 4

$1$ .

Answer 5

Problem 5

Terms approach $1/2\ne0$ , so it diverges.

Answer 6

Problem 6

Converges because $p=5/4>1$ .

Answer 7

Problem 7

Converges by comparison with $1/n^2$ .

Answer 8

Problem 8

Ratio with $1/n^2$ approaches $2$ ; converges.

Answer 9

Problem 9

Conditional convergence.

Answer 10

Problem 10

Ratio limit $0$ ; converges absolutely.

Answer 11

Problem 11

Root limit $1/3$ ; converges absolutely.

Answer 12

Problem 12

Require $1/(N+1)<0.005$ , so $N\ge200$ .

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?

Source & rights

Original instruction with traceable references.

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