# An Introduction to Summation Notation: Definition, Explanation, and Examples

Summation notation is an important mathematical concept that allows for the concise representation of repeated addition. This can be useful for students and teachers, making calculations easier to understand.

Additionally, you can use summation notation to calculate the sum of a series of numbers. This can be helpful in various situations, such as when working with financial data or calculating averages.

This blog post will explain what summation notation is and how to calculate it. We’ll also cover the basics of using summation notation.

## What Is Summation Notation?

Summation notation is a mathematical way of representing the total of a given set of numbers. It allows for quick and easy calculation of large sums, which can be helpful in various situations. Sigma notation is a specific type of summation notation that uses the Greek letter sigma “∑” as its symbol.

Sigma notation is particularly useful for representing sums of large numbers. For example, if you have a set of hundreds of numbers, sigma notation allows you to calculate the sum of those numbers incredibly quickly.

## The Summation Notation Formula

Summation notation is a mathematical formula used to calculate the sum of a given set of numbers. The formula consists of five parts: the upper limit (the number of terms being added together), the index of summation (usually represented by i=, x=, or n=), the lower limit (the first value of n), the summation symbol (sigma “Σ”), and the function itself.

In the example above, n is the upper limit, i is the index of summation, and 1 is the lower limit. The function is f(x).

## The Basics of Summation Notation

Sigma notation is a way of writing out a long sum in a compact form. This can be very helpful when dealing with sums that are lengthy or have many terms. To calculate a sum using sigma notation, you simply take the total number of terms and multiply that sum by the value of each term.

With sigma notation, the sigma is placed before each term in the sum, with a space between it and the next term.

## How to calculate summation?

You can solve the problems of summation notation easily by using the summation rules. Let us take some examples of summation.

Example 1: By using rules

In the example below, the function is 5x^3 + 12x – 20 and we are being asked to sum the first 9 terms starting with x=1. So we can calculate the sum of the given summation function for each term separately using arithmetic rules.

Solution

Step 1: First, take the given summation function and apply the notation to it.

Step 2: Now apply the summation notation with each function term separately with the help of sum and difference rules.

Step 3: Now evaluate the sum of each term separately.

Step 4: Now put the above values in the equation to calculate the sum of the given expression.

You can also calculate the summation notation of any function with the help of a sigma notation calculator

Example 2: By placing the values

In the example below, the function is 2x2 – x3 + 2 and we are being asked to sum the first 6 terms starting with x=1. So we can calculate the sum of the given summation function for x = 1, 2, 3, 4, 5, and 6.

Solution

Step 1: First, take the given summation function and apply the notation of summation to it.

Step 2: Now substitute the values of x from 1 to 6 into the given expression, one-by-one.

Step 4: Now add all the above results to calculate the total sum of the given expression.

## Sum up

You have witnessed that summation notation is not a difficult topic after all. Summation notation is a mathematical technique for calculating a larger sum. Now you can solve problems of summation notation with the help of the above-discussed examples.

WorldWise Tutoring also has tutors who are highly proficient in math topics like this and can help. Find a tutor today!