#sequences

40. Sequences, Series, Summability

This volume studies convergence, divergence, and summation methods for sequences and series. It extends classical analysis with refined convergence concepts and summability techniques. Part I. Sequences Chapter 1. Basic Properties of Sequences 1.1 Definitions and examples 1.2 Convergence and divergence 1.3 Boundedness and monotonicity 1.4 Subsequences 1.5 Limit superior and inferior Chapter 2. Cauchy Sequences 2.1 Definition 2.2 Completeness of ℝ 2.3 Equivalence with convergence 2.4 Examples 2.5 Applications Chapter...