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Mathematical Analysis Fundamentals by Agamirza Bashirov

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Chapter 3

Convergence

Abstract

Chapter 3 deals with convergence of real numbers. It starts with a definition of convergence and its discussion. Next, the concept of Cauchy sequence is introduced and the equivalence of convergence and being Cauchy sequence in the system of real numbers is proved. Convergence is interrelated to distinct features of the system of real numbers. The important concept of subsequence, limit superior and limit inferior are introduced. Numerical series are presented as another form of sequences. Some basic tests for convergence and for divergence of numerical series are proved. Absolute and conditional forms of convergence of numerical series are discussed. The similarity of absolutely convergent series and finite sums ...

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