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
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
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