What are infinite series used for?

Sep 26, 2014

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:

$3.333 \ldots$

by splitting into individual decimals,

$= 3 + 0.3 + 0.03 + 0.003 + \cdots$

by rewriting into a form of geometric series,

$= 3 + 3 \left(\frac{1}{10}\right) + 3 {\left(\frac{1}{10}\right)}^{2} + 3 {\left(\frac{1}{10}\right)}^{3} + \cdots$

by using the formula for the sum of geometric series,

$= \frac{3}{1 - \frac{1}{10}} = \frac{10}{3}$

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