Calculus/Definition of a Series

Definition of a SeriesEdit

Series
A series is the sum of the terms in a sequence.

For a sequence  , the series   would be  . This is true for all series, as it follows from the definition. Only adding a sub-sequence is called a partial sum.

Summation NotationEdit

Purely using the prior definition of a series is possible, but unwieldy. Instead we can again put to use summation notation, which was partially covered in the section on 'integrals'. Some common properties and identities are outlined here.

IdentitiesEdit

  where   is some constant.
 
 
 

PropertiesEdit

  This is the adding of sums.
  Note that this is essentially the distributive property, so this will work for anything that follows the distributive property, even non-constant terms.