infinite sum
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A series is a group of similar things that are all related to the same topic.

In mathematics, a series is the adding of a sequence, a list of (usually never-ending) mathematical objects (such as numbers). It is sometimes written as ,[1] which is another way of writing .

For example, the series [2] corresponds to the following sum:

Here, the dots mean that the adding does not have a last term, but goes on to infinity.

If the result of the addition gets closer and closer to a certain limit value, then this is the sum of the series. For example, the first few terms of the above series are:

From these, we can see that this series will have 2 as its sum.

However, not all series have a sum. For example. a series can go to positive or negative infinity, or just go up and down without settling on any particular value. In which case, the series is said to diverge.[3] The harmonic series is an example of a series which diverges.



  1. "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-08-30.
  2. Weisstein, Eric W. "Series". Retrieved 2020-08-30.
  3. "Infinite Series". Retrieved 2020-08-30.