**ERIC Number:**EJ938184

**Record Type:**Journal

**Publication Date:**2006-Nov

**Pages:**6

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0746-8342

The Divergence of Balanced Harmonic-Like Series

Lutzer, Carl V.; Marengo, James E.

College Mathematics Journal, v37 n5 p364-369 Nov 2006

Consider the series [image omitted] where the value of each a[subscript n] is determined by the flip of a coin: heads on the "n"th toss will mean that a[subscript n] =1 and tails that a[subscript n] = -1. Assuming that the coin is "fair," what is the probability that this "harmonic-like" series converges? After a moment's thought, many people answer that the probability of convergence is 1. This is correct (though the proof is nontrivial), but it doesn't preclude the existence of a "divergent" example. Indeed, Feist and Naimi provided just such an example in 2004. In this paper, we construct an uncountably infinite family of examples as a companion result.

Descriptors: Probability, Mathematics Instruction, College Mathematics, Mathematical Concepts, Validity, Mathematical Logic, Problem Solving

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A