| 单词 | convergent series |
| 释义 | convergent series A series a1 + a2 + … + ai + …, for which a partial sum Sn = a1 + a2 + … + an tends to a finite (or zero) limit as n tends to infinity. This limit is the sum of the series. For example, the series 1 + 1/2 + 1/4 + 1/8 + … (with the general term ai equal to (1/2)i-1) tends to the limit 2. A series that is not convergent is said to be a divergent series . In such a series the partial sum tends to plus or minus infinity or may oscillate. For example, the series 1 + 1/2 + 1/3 + 1/4 + … (with ai equal to 1/i) is divergent. As can be seen from this latter example, a series may be divergent even if the individual terms ai tend to zero as i tends to infinity |
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