Series facts for kids
A series is a group of similar things that are all related to the same topic. In mathematics, a series is when you add up a list of numbers, one after another. This list can sometimes go on forever!
Imagine you have a list of numbers like 1, 2, 3, 4, and so on. If you add them all up (1 + 2 + 3 + 4 + ...), that's a series.
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What is a Math Series?
In math, a series is like a long addition problem. You take a group of numbers and add them together. Sometimes, this list of numbers never ends.
For example, look at this series:
- 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + ...
The "..." means the numbers keep going on and on, forever!
Finding the Sum of a Series
When you add the numbers in a series, the total might get closer and closer to a certain value. If it does, that value is called the sum of the series.
Let's look at the example again and see what happens when we add the numbers step by step:
- 1 + 1/2 = 1 and 1/2
- 1 + 1/2 + 1/4 = 1 and 3/4
- 1 + 1/2 + 1/4 + 1/8 = 1 and 7/8
- 1 + 1/2 + 1/4 + 1/8 + 1/16 = 1 and 15/16
- 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 1 and 31/32
- 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 = 1 and 63/64
- 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 = 1 and 127/128
Do you see a pattern? The total gets closer and closer to 2. So, the sum of this series is 2.
When a Series Doesn't Have a Sum
Not all series have a sum that they get close to. Some series just keep getting bigger and bigger (going to positive infinity), or smaller and smaller (going to negative infinity). Others might just jump around without settling on a number.
When a series doesn't settle on a specific sum, we say it diverges. This means it doesn't have a final, fixed total. The harmonic series is an example of a series that diverges.
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