MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Consider the five infinite series below.
(a) For each series, compute n→∞liman, where an denotes the general term of the series.
(b) Using only the limits you found in part (a), classify each series into one of the following three categories and justify your decision.
1. "Definitively diverges"
2. "Definitively converges"
3. "Limit test inconclusive"
(c) Select one series that fell into Category 3 in part (b).
(i) Explain why the limit test alone cannot determine convergence for that series.
(ii) Name a different convergence test that could be applied and briefly describe how it would address the limitation of the limit test.