# Infinite Geometric Series Calculator

A **geometric series** is a series where every term bears a constant ratio to its preceding term. The geometric series is represented as a, ar, ar^{2}, ar^{3},...ar^{n}.

## What is an Infinite Geometric Series Calculator?

'Cuemath's Infinite Geometric Series Calculator' is an online tool that assists in calculating the sum of an infinite geometric progression. Cuemath's online infinite geometric series calculator helps you to calculate the sum of an infinite geometric series in a few seconds.

## How to Use Infinite Geometric Series Calculator?

Please follow the below steps to find the sum of infinite geometric series::

**Step 1:**Enter the value of the first term and the value of the common ratio in the given input boxes.**Step 2:**Click on the**"Calculate"**button to find the sum of the infinite series.**Step 3:**Click on the**"Reset"**button to clear the fields and enter the different values.

## How to Find Infinite Geometric Series Calculator?

Infinite geometric series is an infinite progression with first term a_{1} and common ratio (r) and if the value of r lies between 0 and 1, that is 0 < r < 1 then we can calculate the sum of the infinite geometric series with the help of below-given formula:

S_{∞} = a_{1} / (1 - r)

**Solved Example:**

Calculate the sum of given infinite geometric series:

16, 8, 4, 2, 1, 0.5, ................

**Solution:**

In the given geometric series

The value of first term a_{1} = 16

And the common ratio r = 0.5

So, the sum of infinite series is = S_{∞} = a_{1} / (1 - r)

S_{∞} = 16 / (1 - 0.5)

S_{∞} = 16 / 0.5

S_{∞} = 32

Thus, the sum of given infinite series is 32.

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