Cauchy’s Cours d’analyse pp 85-115 | Cite as

# On convergent and divergent series. Rules for the convergence of series. The summation of several convergent series.

[114]We call a series an indefinite sequence of quantities, u0, u1, u2, u3, …, which follow from one to another according to a determined law. These quantities themselves are the various terms of the series under consideration. Let be the sum of the first *n* terms, where *n* denotes any integer number. If, for ever increasing values of *n*, the sum *s* _{ n } indefinitely approaches a certain limit *s*, the series is said to be *convergent*, and the limit in question is called the sum of the series. On the contrary, if the sum *s* _{ n } does not approach any fixed limit as n increases indefinitely, the series is *divergent*, and does not have a sum. In either case, the term which corresponds to the index *n*, that is *u* _{ n }, is what we call the *general term*. For the series to be completely determined, it is enough that we give this general term as a function of the index *n*.

## Keywords

Convergent Series Negative Term Positive Term Geometric Progression Integer Power## Preview

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