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A NOTE ON THE SUM OF RECIPROCALS

  • YUCHEN DING (a1) and YU-CHEN SUN (a2)

Abstract

We prove that, given a positive integer $m$ , there is a sequence $\{n_{i}\}_{i=1}^{k}$ of positive integers such that

$$\begin{eqnarray}m=\frac{1}{n_{1}}+\frac{1}{n_{2}}+\cdots +\frac{1}{n_{k}}\end{eqnarray}$$
with the property that partial sums of the series $\{1/n_{i}\}_{i=1}^{k}$ do not represent other integers.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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