Practical Session 4: Convergence Tests for Series

This practical session develops students' skills in applying convergence tests for infinite series through active problem-solving. The material is intended for students studying mathematical analysis who are familiar with series concepts.

The session covers all major convergence tests through structured problems. Students practice the Ratio Test on series with factorials and exponentials. The Root Test is applied to series with terms raised to powers. The Integral Test connects series to improper integrals, enabling analysis of p-series. The Alternating Series Test addresses series with alternating signs, including error estimation.

Problems progress from straightforward applications to more challenging mixtures requiring test selection. Each problem includes complete step-by-step solutions. The session concludes with homework problems and a summary of key tests.