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A Bouquet of Series

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Book cover Limits, Series, and Fractional Part Integrals

Part of the book series: Problem Books in Mathematics ((PBM))

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Abstract

This chapter offers the reader a bouquet of problems with a flavor towards the computational aspects of infinite series and special products, many of these problems being new in the literature. These series, linear or quadratic, single or multiple, involve combinations of exotic terms, special functions, and harmonic numbers and challenge the reader to explore the ability to evaluate an infinite sum, to discover new connections between a series and an integral, to evaluate a sum by using the modern tools of analysis, and to investigate further.

Even if we have thousands of acts of great virtue to our credit, our confidence in being heard must be based on God’s mercy and His love for men. Even if we stand at the very summit of virtue, it is by mercy that we shall be saved.

St. John Chrysostom (347–407)

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Notes

  1. 1.

    Joseph Wolstenhome (1829–1891) was an English mathematician and the author of Mathematical problems.

  2. 2.

    The function \(f(x) = -\frac{\ln (1-x)} {1-x}\) is known in the mathematical literature as thegenerating function for the nth harmonic number.

  3. 3.

    The solution of this problem is based on a joint work with H. Qin.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Ovidiu Furdui

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  1. Ovidiu Furdui
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Furdui, O. (2013). A Bouquet of Series. In: Limits, Series, and Fractional Part Integrals. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6762-5_3

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