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May 2020 A Pascal Triangle Type Calculation for a Particular Infinite Series
Simon Aloff, Michael Miniere
Missouri J. Math. Sci. 32(1): 61-70 (May 2020). DOI: 10.35834/2020/3201061

Abstract

In general, finding the sum of an infinite series is not always possible. However, there are infinite series whose sums can be computed. In our earlier paper, we derived a formula for computing the sum of a type of polylogarithm series involving multinomial coefficients. In this paper, we show that the formula leads to an elementary computation for the series $\sum_{k=1}^{\infty}\frac{k^n}{a^k}$ involving numbers obtained by a method similar to Pascal's triangle. We also show that our result is the number of ways of distributing $n$ distinct objects in $n$ or fewer distinct nonempty cells.

Citation

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Simon Aloff. Michael Miniere. "A Pascal Triangle Type Calculation for a Particular Infinite Series." Missouri J. Math. Sci. 32 (1) 61 - 70, May 2020. https://doi.org/10.35834/2020/3201061

Information

Published: May 2020
First available in Project Euclid: 2 July 2020

MathSciNet: MR4118651
Digital Object Identifier: 10.35834/2020/3201061

Subjects:
Primary: 11B73
Secondary: 11M35

Rights: Copyright © 2020 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.32 • No. 1 • May 2020
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