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Fun with Sign

Published online by Cambridge University Press:  23 January 2015

Li Zhou
Li Zhou*
Affiliation:
Department of Mathematics, Polk State College, Winter Haven, FL 33881, USA e-mail: [email protected]
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Extract

When I was teaching calculus recently, an exercise in the textbook [1, p. 687, qn. 3] asked students to find the Taylor series of cosx centred at π/4. My students were able to find the series

but wondered how to take care of the sign changes, in order to express the series in I.-notation. They were quite puzzled after finding that the answer given in [I] is

The exponent n (n + 1)/2 seemed a rabbit out of the hat! This article is the result of trying to answer their question satisfactorily, and to have some serious fun. Readers are invited to try two teasers first before reading for their solutions.

Type
Articles
Information
The Mathematical Gazette , Volume 97 , Issue 540 , November 2013 , pp. 465 - 473
Copyright
Copyright © The Mathematical Association 2013

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References

1. Larson, R. and Edwards, B. H., Calculus (9th edn.), Brooks/Cole, Cengage Learning (2010).Google Scholar
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4. Lewis, B., More power to Pascal, Math. Gaz. 92 (November 2008) pp. 454–465.Google Scholar
5. Pólya, G. and Szegö, G., Problems and theorems in analysis II, Springer (1976).Google Scholar