Series and sequence are the basic components of mathematics. A sequence is a sequential representation of any kind of data while a series is a summation of the elements of a sequence. We usually donate the series using the variable S.

Finding the sum of a series is a complicated mathematical operation that becomes difficult while performing it manually. However, in the world of high-performance computing, it has become an easier task by using MATLAB’s built-in **symsum()** function.

Follow this article to learn how to compute the symbolic sum of a series in MATLAB using the **symsum() **function.

## What is a Series?

As mentioned earlier a series is a summation of a sequence’s elements. In mathematics, it is considered as a sequence having N terms x1,x2,x3,…xN and can be denoted as:

Here, **xi** represents the terms of the above sequence at the **ith** location.

## How to Find the Symbolic Sum of a Series in MATLAB Using the symsum() Function?

MATLAB is a high-performance computing tool that provides us with a built-in **symsum() **function to compute the sum of the symbolic series. This function accepts one or more inputs and returns a scalar value that represents the computed summation of the given series.

## Syntax

There are different syntaxes of the **symsum() **function in MATLAB, which are given below:

S = symsum(f,k)

Here,

The function **S = symsum(f,k,a,b)** computes the series sum denoted by f with respect to summation index k ranges from the lower bound a to the upper bound b. If k is not specified, the function uses the variable determined by **symsum** as an index. If f behaves like a constant the default index will be x.

**Note: **The function **symsum(f,k,a,b) **is equivalent to **symsum(f,k,[a,b])** and **symsum(f,k,[a;b])**.

The function **S = symsum(f,k)** determines the indefinite summation of the series f over the index k satisfying the relation:

## Examples

Consider some examples to practically understand the working of the **symsum()** function to determine the sum of the series in MATLAB.

## Example 1: How to Find the Sum of the Series for the Specified Bounds Using the symsum(f,k,a,b) Function?

This example calculates the finite sum of the given series from lower bound a=0 to upper bound b=20 using the **symsum(f,k,a,b)** function in MATLAB.

S = symsum(1/(k^2+1),k,0,20)

## Example 2: How to Find the Indefinite Sum of the Series Using the symsum(f,k) Function?

In this example, we compute the indefinite sum of the given series f over k using the **symsum(f,k)** function.

S = symsum(k^2,k)

## Conclusion

A series is the summation of a sequence’s elements. Manually, it is a complicated task to find the sum of a series. However, in MATLAB, you can calculate it quickly using the **sysum() **function. This guide has presented different syntaxes of the **symsum()** function in MATLAB and provided examples for each syntax to help us understand this function working.