the series is convergent, the (necessarily unique) number is called the sum of the series.

The same notation
:is used for the series, and, if it is convergent, to its sum. This convention is similar to that which is used for addition: denotes the operation of adding and as well as the result of this addition, which is called the sum of and .

Any series that is not convergent is said to be divergent or to diverge.

Examples of convergent and divergent series

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