Infinite series
Imagine you have a bag of candy, and you keep taking out one piece at a time. You keep taking out candy and never stop.
An infinite series is like that, but instead of candy, you have numbers. You keep adding numbers together and never stop.
For example, if we start with 1 and keep adding fractions that have a numerator of 1 and a denominator that is increasing by one each time, we get the following infinite series:
1 + 1/2 + 1/3 + 1/4 + 1/5 + …
This series never stops because we can always find another fraction to add.
It's important to note that not all infinite series have a definite sum. Some infinite series keep getting larger and larger and never settle down to a specific value. Others might alternate between positive and negative terms, making their sum oscillate between two values.
In maths, we have ways of working out if a series has a definite sum or not. And if it does, we can find a formula that tells us exactly what that sum is.
An infinite series is like that, but instead of candy, you have numbers. You keep adding numbers together and never stop.
For example, if we start with 1 and keep adding fractions that have a numerator of 1 and a denominator that is increasing by one each time, we get the following infinite series:
1 + 1/2 + 1/3 + 1/4 + 1/5 + …
This series never stops because we can always find another fraction to add.
It's important to note that not all infinite series have a definite sum. Some infinite series keep getting larger and larger and never settle down to a specific value. Others might alternate between positive and negative terms, making their sum oscillate between two values.
In maths, we have ways of working out if a series has a definite sum or not. And if it does, we can find a formula that tells us exactly what that sum is.
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