Assess students' ability to determine convergence or divergence of improper integrals and infinite series, with emphasis on borderline and conditional cases. Tasks require selecting and justifying appropriate tests (comparison, limit comparison, p-test, integral test, ratio/root, alternating series test, Dirichlet/Abel where relevant), distinguishing absolute versus conditional convergence, and analyzing singularities or infinite integration limits. Include problems such as p-series at p=1, alternating modifications, integrals with endpoint singularities and infinite intervals, and cases where common tests are inconclusive; require clear, rigorous explanation of why a chosen test applies or fails and a reasoned conclusion.