Question

What are infinite series used for?

Answer 1

It is very tough to answer such a general question, but I will give it a shot. Infinite series allow us to add up infinitely many terms, so it is suitable for representing something that keeps on going forever; for example, a geometric series can be used to find a fraction equivalent to any given repeating decimal such as:

`3.333...`

by splitting into individual decimals,

`=3+0.3+0.03+0.003+cdots`

by rewriting into a form of geometric series,

`=3+3(1/10)+3(1/10)^2+3(1/10)^3+cdots`

by using the formula for the sum of geometric series,

`=3/{1-1/10}=10/3`

The knowledge of geometric series helped us find the fraction fairly easily. I hope that this was helpful.