“Arithmetic Series”的概念、定义、习题解题方法及翻译-数学辞典

单词

Arithmetic Series

释义

Arithmetic Series

An arithmetic series is the Sum of a Sequence , , 2, ..., in which each term is computed from theprevious one by adding (or subtracting) a constant. Therefore, for ,

(1)

The sum of the sequence of the first

terms is then given by



			(2)

Using the Sum identity

(3)

then gives

(4)

Note, however, that

(5)

(6)

times the Gauß

used as a schoolboy tosolve the problem of summing the Integers from 1 to 100 given as busy-work by his teacher. While hisclassmates toiled away doing the Addition longhand, Gauss wrote a single number, the correct answer

(7)

on his slate. When the answers were examined, Gauss's proved to be the only correct one.

See also Arithmetic Sequence, Geometric Series, Harmonic Series, Prime Arithmetic Progression

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.

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

Courant, R. and Robbins, H. ``The Arithmetical Progression.'' §1.2.2 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 12-13, 1996.

Pappas, T. The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 164, 1989.

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