A geometric series is a series for which the ratio of each two consecutive terms is a constant
function of the summation index , say . Then the terms are of the form , so . If
, with , 2, ..., is a Geometric Sequence with multiplier and , then the geometric
series

(1) |

(2) |

(3) |

(4) |

so

(5) |

(6) |

**References**

Abramowitz, M. and Stegun, C. A. (Eds.).
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, p. 10, 1972.

Arfken, G. *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press, pp. 278-279, 1985.

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

Courant, R. and Robbins, H. ``The Geometric Progression.'' §1.2.3 in
*What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.*
Oxford, England: Oxford University Press, pp. 13-14, 1996.

Pappas, T. ``Perimeter, Area & the Infinite Series.'' *The Joy of Mathematics.*
San Carlos, CA: Wide World Publ./Tetra, pp. 134-135, 1989.

© 1996-9

1999-05-25