*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

Consider the sum

(1) |

(2) |

(3) |

(4) |

(5) | |||

(6) |

Then

(7) |

A modified sum was considered by Elbert (1973):

(8) |

(9) |

(10) |

(11) | |||

(12) |

Then

(13) |

**References**

Drinfeljd, V. G. ``A Cyclic Inequality.'' *Math. Notes. Acad. Sci. USSR* **9**, 68-71, 1971.

Elbert, A. ``On a Cyclic Inequality.'' *Period. Math. Hungar.* **4**, 163-168, 1973.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/shapiro/shapiro.html

Mitrinovic, D. S.; Pecaric, J. E.; and Fink, A. M. *Classical and New Inequalities in Analysis.* New York: Kluwer, 1993.

© 1996-9

1999-05-26