# Summation Convergence Calculator

Sum of the Series (S): -

## Introduction

Welcome to the Summation Convergence Calculator tutorial. This guide will walk you through creating an HTML calculator to find the sum of a series using the formula S = a / (1 – r). Whether you’re a beginner or an experienced coder, you’ll find this step-by-step tutorial helpful in building a functional calculator.

## How to Use

To use the Summation Convergence Calculator, follow these steps:

1. Input the value of the first term (a) into the designated field.
2. Input the value of the common ratio (r) into the appropriate field.
3. Click the “Calculate” button to compute the sum of the series (S).
4. The result will be displayed on the screen.

## Formula

The formula used in this calculator is:

S = a / (1 – r)
• S: Sum of the series
• a: First term
• r: Common ratio

## Example

Let’s illustrate how to use the calculator with an example: Suppose a = 5 and r = 0.2. Plug these values into the formula:

S = 5 / (1 – 0.2) S = 5 / 0.8 S = 6.25

So, for these inputs, the sum of the series (S) is 6.25.

Q1: Can I use this calculator for any series?

Yes, you can use this calculator for geometric series where the common ratio (r) is not equal to 1.

Q2: What happens if I enter invalid values for a and r?

The calculator will return an error or display “NaN” (Not-a-Number) if you input non-numeric values or if the denominator becomes zero.

Q3: Can I use this code on my website?