# Infinite Series Calculator

A series is defined as the sum of a given sequence. The sum of a particular part of a sequence is called its partial sum.

## What is Infinite Series Calculator?

'Cuemath's Infinite Series Calculator' is an online tool that helps to calculate the summation of infinite series for a given function. Cuemath's online Infinite Series Calculator helps you to calculate the summation of infinite series for a given function in a few seconds.

## How to Use Infinite Series Calculator?

Please follow the steps below on how to use the calculator:

**Step 1:**Enter the function in the given input box.**Step 2:**Click on the**"Find"**button to find the summation of the infinite series**Step 3:**Click on the**"Reset"**button to clear the fields and enter a new function.

## How to Find Infinite Series Calculator?

The summation is defined as the addition of a large number of data that are a concerned sequence of any kind of numbers, called addends or summands. ∑ the symbol is used for a total sum which is called sigma to denote summation.

The sum of the infinite series of an arithmetic series is undefined.

The sum to infinity for a geometric series is undefined when |r| > 1, where 'r' is the common ratio.

The sum to infinity for a geometric series is \({S_\infty } = \frac{a}{1-r}\) when |r| < 1 and 'a' is the first term.

**Solved Example:**

Find sum of infinite series for a function \(\sum_{x =1}^{∞} \frac{5}{2^x}\)

**Solution:**

x = 1, first term a = 5 / 2

= 5

common ratio r = (5/2)/(5/4)

= 1/2

\({S_\infty } = \frac{a}{1-r} = \frac{\frac{5}{2}}{{1 - \frac{1}{2}}}\)

= 5

Similarly, you can try the calculator to infinite series for the following functions:

- \(\sum_{x =1}^{∞} \frac{3}{2^x}\)
- \(\sum_{x = 0}^{∞} \frac{5}{3^x}\)