# What is Summation and how to apply summation on functions?

What is Summation and how to apply summation on functions?

Summation is used to write a large sequence or numbers of terms in a short method. It is widely used in mathematics, as in calculus the use of summation is very important.

In this post we will learn about the definition, basic concept and how to calculate summation through a lot of examples.

## What is Summation?

Summation is a process of addition of a sequence of any type of numbers. It is adding up a series of items. A summation is also called sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. It is the sequential addition on a set of numbers. It is simple to do for a few numbers, but can get more complex with fraction, real numbers or algebra. It can also sum function, matrices and vectors. Summation notation is allowing expression that contain a sum to be expressed in simple compact manner. It instructs us to sum elements of a sequence. The variable of summation is represented by an index which is placed beneath the summation sign.

## Summation Notation

The upper-case Greek letter sigma written as Σ is used to denote the sum of a set of numbers.

Summation notation as some general formulas.

## Rule of Summation

Some basic rules of summation are

### Constant rule

When there is a constant inside the summation, we take that constant outside the summation notation.

Example

Solution

Step 1: Take constant outside the summation notation.

Step 2: Solve summation.

### Sum rule

When there are two functions having addition notation we use this rule, according to this rule we apply the summation notation separately on both the functions.

### Difference rule

When there are two functions having subtraction notation we use this rule, according to this rule we apply the summation notation separately on both the functions.

## How to do summation?

Summation Calculator can be used to perform summation on a function. Let us take some examples in order to learn how to calculate summation.

## Summary

In this post we have learnt about the definition, notation, rules and how to calculate Summation with the lot of examples. Once you grabbed the knowledge of this topic you can easily solve the problems related to summation.