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Rearranging terms of a harmonic-like series
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1. INTRODUCTION
The commutative law of addition is familiar to our students. However, if the sum involves an infinite number of terms, the commutative law might not be true. This is indeed a surprise to many! In this paper we will study one example of a series which illustrates the failure of the commutative law. Our series is
3. FINAL REMARKS
Theorem (b) from Section 1 promised that our conditionally convergent series (1) could be rearranged so that it converged to any number whatsoever. The theorem just proved in Section 2 showed how to rearrange the terms so that the sum of the series ...
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