Series

Infinite sum

A series is a group of several things that are all about the same thing, or are intentionally similar.

In mathematics, a series is the adding of a never ending mathematical sequence (a list of numbers). For example:

${\displaystyle 1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+{\frac {1}{32}}+{\frac {1}{64}}+{\frac {1}{128}}+\ldots }$

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, this is the sum of the series.

${\displaystyle 1+{\frac {1}{2}}=1{\frac {1}{2}}}$

${\displaystyle 1+{\frac {1}{2}}+{\frac {1}{4}}=1{\frac {3}{4}}}$

${\displaystyle 1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}=1{\frac {7}{8}}}$

${\displaystyle 1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}=1{\frac {15}{16}}}$

${\displaystyle 1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+{\frac {1}{32}}=1{\frac {31}{32}}}$

${\displaystyle 1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+{\frac {1}{32}}+{\frac {1}{64}}=1{\frac {63}{64}}}$

${\displaystyle 1+{\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+{\frac {1}{32}}+{\frac {1}{64}}+{\frac {1}{128}}=1{\frac {127}{128}}}$

This series will have 2 as its sum. However, not all series have a sum.