| 释义 |
Geometric SeriesA geometric series  is a series for which the ratio of each two consecutive terms  is a constantfunction 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 geometricseries
 | (1) |
 | (2) |
 | (3) |
so
 | (5) |
 , then
 | (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. |
