# Science:Infinite Series Module/Units/Unit 1/1.2 Sigma Notation/1.2.01 Introduction to Sigma Notation

In many areas of mathematics, we are given an infinite sequence

${\displaystyle \{a_{n}\}_{n=1}^{\infty }}$

and we need to add its elements together

${\displaystyle a_{1}+a_{2}+a_{3}+\ldots +a_{n}+\ldots }$

which would produce what we will refer to as an infinite sum or infinite series. In producing this infinite sum, we are led to the following initial questions:

• Is there a convenient notation that we can use to represent an infinite sum?
• What properties would the sum have?
• Can we find equivalent representations of the sum?

The last question is of particular importance when

• applying formulas to infinite sums, and
• performing algebraic manipulations upon equations with multiple sums,

as we will see later in the module.