infinite sum From Wikipedia, the free encyclopedia
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.
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