An Introduction to Summation Notation Examples with Video

Introduction to summation notation will give you an overview of this very important part of mathematics. In mathematics and statistics, the summation is frequently used to summarize a group or series of numbers that are to be summed up. The sum of two or more numbers is a general task in daily life such as buying some products like soap and shampoo then you have to pay the summed amount of both products. You should find it worthy to find the introduction to summation notation.

When the addition of several functions or terms becomes lengthy or difficult then a term summation can be used. In this post, we will study the definition, rules, and examples of summation with a lot of examples.

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What is the summation?

In mathematics, the summation is a notation that allows us to write lengthy terms of sum in one expression. It is also known as a sigma notation. It is denoted by a “∑” symbol. All the terms of sum and series can be adjusted in a single sigma notation.

The expression used to denote summation is:

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  • The expression, “∑” is the sigma notation.
  • “i” is the index.
  • “i = 1” is the first term.
  • “n” is the last term.
  • “xi” is the nth term.

The expression of summation can be used for:

  1. Simple summation
  2. Sigma notation

In simple summation, you have to add a series of numbers like 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. Any kind of sum of various numbers or terms is referred to simple summation. While sigma notation is used to perform the accurate sequence of functions with initial and final values.

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A sigma notation calculator can be used to solve the problems of simple summation and sigma notation with a single click.

Rules of summation

There are several rules of summation, let us discuss them briefly.

1.   Constant rule of summation

According to the constant rule of summation, the constant term must be summed up for n times to find the sum of the series. The general expression of this rule of summation is:

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Where A is any constant.


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2.   Sum rule of summation

According to the sum rule of the summation, the notation of summation must be applied to each function separately. The general expression of this rule of summation is:

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Find the summation of x2 + 2x if the starting value is 1 and the final value is 6.


Step 1: First of all, write the sigma notation of the given function.

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Step 2: Apply the sum rule of summation

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Step 3: Now find the summation of both terms.

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Step 4: Now add both the summations.





Difference rule of summation

According to the different rules of the summation, the notation of summation must be applied to each function separately. The general expression of this rule of summation is:

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Find the summation of 2x2 – 4x if the starting value is 1 and the final value is 7.


Step 1: First of all, write the sigma notation of the given function.

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Step 2: Apply the difference rule of summation

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Step 3: Now find the summation of both terms.

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Step 4: Now subtract both the summations.

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How to calculate summation?

The problems of the summation function can be solved easily by using the rules of summation. Let us take some examples of summation.


Find the summation of 2x2 + 3x – 6 if the starting value is 1 and the final value is 8.


Step 1: First of all, write the sigma notation of the given function.

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Step 2: Apply the sum and difference rules of summation

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Step 3: Now find the summation of the above expressions one by one.


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Step 4: Now substitute the above terms in the given expression.

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In this post, we have learned all the basics of summation along with a lot of examples. Now after reading the above post on introduction to summation notation, you can solve any problem with simple summation and sigma notation easily. You can grab all the basics of summation from this post, as well as an introduction to sigma notation.

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