Inspiring Examples in Rearrangements of Infinite Series

Autor/in	Ramasinghe, W.
Titel	Inspiring Examples in Rearrangements of Infinite Series
Quelle	In: International Journal of Mathematical Education in Science and Technology, 33 (2002) 1, S.137-146 (10 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
Schlagwörter	Teaching Methods; Mathematics Instruction; Learning Processes; Mathematical Concepts; College Mathematics; Student Motivation; Mathematics Teachers; Calculus; Comprehension; Computation + Suchen Sie Ihr Suchwort? Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics lessons; Mathematikunterricht; Learning process; Lernprozess; Schulische Motivation; Mathematics; Teacher; Teachers; Mathematik; Lehrer; Lehrerin; Lehrende; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Verstehen; Verständnis
Abstract	Simple examples are really encouraging in the understanding of rearrangements of infinite series, since many texts and teachers provide only existence theorems. In the absence of examples, an existence theorem is just a statement and lends little confidence to understanding. Iterated sums of double series seem to have a similar spirit of rearrangements of series though they are not the same. Therefore learning about iterated sums of double series will help the understanding of the rearrangements of series. Without simple examples, which is the case with many texts, theorems about iterated sums do not contribute much to our understanding. Many students and perhaps some teachers would be discouraged by this in the learning process. In this note, several inspiring examples are presented to show that infinite sums indeed behave very differently from finite sums. (Author).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10