A series is defined as the sum of terms in a sequence.

• The sum of all terms in an infinite sequence is called an infinite series
• 
• The sum of a specific terms of a sequence is called a finite sequence
• 

Series can also be expressed using Summation Notation or Sigma Notation  

The examples above can be written as

Where i is the Index of Summation,  and 14 are the Upper Limit of

Summation and 1 and 5 are the Lower Limit of Summation.

Example:

Properties of Sums:

• 

• 
  

• 
  

Note: It is important to keep in mind that one summation may be written in many different ways by rearranging the upper and lower limits of the summation

When the finite series is the sum of the first n terms in a sequence, it is called the nth Partial Sum and is  denoted by which is equal to

Example:

(sum of first 5 terms)

(sum of first 42 terms)

Note: Partial sums can be used to express non partial sum summations

                              
If you are still struggling with Summations, here are a few links you can check out:
http://www.columbia.edu/itc/sipa/math/summation.html
http://www.mathsisfun.com/algebra/sigma-notation.html
http://www.mathsisfun.com/algebra/partial-sums.html
https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-series/v/partial-sum-notation
https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-series/v/sigma-notation-sum
https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-series/v/writing-series-sigma-notation