Divergent series – synergy between mathematical fallacies and summation methods
DOI:
https://doi.org/10.55630/mem.2026.55.177-185Keywords:
education, mathematical fallacy, divergent series, summation methods, Cesàro summation, Abel summationAbstract
Summation methods for divergent series are an important element of modern mathematical analysis, meaningfully expanding the classical concept of convergence. The incorrect application of algebraic operations to divergent series leads to mathematical fallacies. The report emphasizes the pedagogical potential of the interaction between summation methods and mathematical fallacies. It is shown that their targeted combination in an educational environment promotes the development of critical and analytical thinking, logical and mathematical culture in students, and an understanding of the important role of definitions and statements in mathematics. Examples of real-world models are considered, demonstrating the applicability of Cesàro’s and Abel’s summation methods.
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