The Sum

(1) |

(2) |

(3) |

The sum of the first few terms of the harmonic series is given analytically by the th Harmonic Number

(4) |

Progressions of the form

(5) |

**References**

Arfken, G. *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press, pp. 279-280, 1985.

Beyer, W. H. (Ed.). *CRC Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press, p. 8, 1987.

Boas, R. P. and Wrench, J. W. ``Partial Sums of the Harmonic Series.'' *Amer. Math. Monthly* **78**, 864-870, 1971.

Honsberger, R. ``An Intriguing Series.'' Ch. 10 in *Mathematical Gems II.*
Washington, DC: Math. Assoc. Amer., pp. 98-103, 1976.

Sloane, N. J. A. Sequence A004080 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

© 1996-9

1999-05-25