Calculus II · Unit 4A · exam

Unit 4A Practice Exam A

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Unit 4A Practice Exam A

Exercise

Find $\lim (4n^2-n)/(2n^2+3)$ .

Exercise

Determine whether $a_n=(-1)^n/n$ converges.

Exercise

Sum $\sum_{n=0}^{\infty}5(1/4)^n$ .

Exercise

Evaluate $\sum_{n=1}^{\infty}1/[n(n+1)]$ .

Exercise

Explain why $\sum n/(2n+1)$ diverges.

Exercise

Classify $\sum1/n^{5/4}$ .

Exercise

Use comparison to classify $\sum1/(n^2+7)$ .

Exercise

Use limit comparison to classify $\sum(2n+1)/(n^3+4)$ .

Exercise

Classify $\sum(-1)^{n-1}/\sqrt n$ as absolute, conditional, or divergent.

Exercise

Use the Ratio Test on $\sum4^n/n!$ .

Exercise

Use the Root Test on $\sum[(n+1)/(3n)]^n$ .

Exercise

How many alternating harmonic terms guarantee error below $0.005$ ?

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?

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