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Calculus Practice: Nth Term Test for Divergence

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2025/2026 Written for academic year
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Put theory into action with 20 carefully designed practice problems based on the Nth Term Test for Divergence. This workbook-style resource gives you space to work through each problem, followed by fully worked-out solutions on a separate page. Covering geometric series, harmonic series, p-series, alternating series, and more, the problems reinforce the key principle: if the limit of terms is not zero, the series diverges; if it is zero, the test is inconclusive. Ideal for self-study or classroom use, these questions help learners build problem-solving skills, recognize common pitfalls, and develop confidence in applying the test. With clear explanations and structured solutions, it’s the perfect companion to the notes document for anyone serious about mastering infinite series in calculus.

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Calculus: Nth Term Test for Divergence



Practice Problems
Apply the Nth Term Test for Divergence to each series below. For each problem, determine whether
the test shows divergence, or if it is inconclusive. Leave space for your work.
P n
1. 2




1
P
2. n




3
P
3. 10n




n
P
4. n+1




5
P
5. n2




P n+2
6. n




√1
P
7. n




n
P
8. n2 +1




1

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