Calculus II · Unit 4A · exam

Unit 4A Practice Exam B

Attempt Unit 4A Practice Exam B under exam conditions, then use the separate worked answer key to diagnose gaps.

Supporting resourceUse this page when the main sequence reveals a specific gap or question.Open the Unit 4A map →

Section overview

Review, practice, exams, and answer keys

What this section is building

Attempt Unit 4A Practice Exam B under exam conditions, then use the separate worked answer key to diagnose gaps.

Notice

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

Decide

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

Avoid

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

Answer key published

Finish first. Then check every answer.

The complete numbered key is online as its own easy-to-find route.

View the complete answer key →

Unit 4A Practice Exam B

Exercise

Analyze the recursive sequence $a_1=1$ , $a_{n+1}=\sqrt{3+a_n}$ , including its possible limit.

Exercise

Find the sum of $\sum_{n=2}^\infty 6(1/3)^n$ .

Exercise

Determine convergence of $\sum1/[n(\ln n)^3]$ .

Exercise

Bound the remainder after $N$ terms of $\sum1/n^4$ .

Exercise

Classify $\sum(n^2+1)/(n^4-3)$ .

Exercise

Classify $\sum(-1)^n n/(n+1)$ .

Exercise

Classify $\sum(-1)^n/(n\ln(n+1))$ .

Exercise

Use the Ratio Test on $\sum n^3/2^n$ .

Exercise

Explain why the Root Test is inconclusive for $\sum1/n^7$ .

Exercise

Give a series that converges conditionally and explain both tests.

Exercise

State and interpret the Cauchy criterion for a series.

Exercise

Explain why numerical evidence cannot prove convergence.

Source & rights

Original instruction with traceable references.

BetterGrades-original; no direct adaptation declared in the verified handoff.

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.

Unit 4A Practice Exam B

Exercise

Analyze the recursive sequence $a_1=1$ , $a_{n+1}=\sqrt{3+a_n}$ , including its possible limit.

Exercise

Find the sum of $\sum_{n=2}^\infty 6(1/3)^n$ .

Exercise

Determine convergence of $\sum1/[n(\ln n)^3]$ .

Exercise

Bound the remainder after $N$ terms of $\sum1/n^4$ .

Exercise

Classify $\sum(n^2+1)/(n^4-3)$ .

Exercise

Classify $\sum(-1)^n n/(n+1)$ .

Exercise

Classify $\sum(-1)^n/(n\ln(n+1))$ .

Exercise

Use the Ratio Test on $\sum n^3/2^n$ .

Exercise

Explain why the Root Test is inconclusive for $\sum1/n^7$ .

Exercise

Give a series that converges conditionally and explain both tests.

Exercise

State and interpret the Cauchy criterion for a series.

Exercise

Explain why numerical evidence cannot prove convergence.

Source & rights

Original instruction with traceable references.

BetterGrades-original; no direct adaptation declared in the verified handoff.

Reference textbooks remain rights-separated and are not published as application assets. Any direct adaptation requires separate identification and attribution.

Finish first. Then check every answer.

Unit 4A Practice Exam B

Related resources

Original instruction with traceable references.

Finish first. Then check every answer.

Unit 4A Practice Exam B

Related resources

Original instruction with traceable references.