Java Program to Find the Sum of the Series 1/1+1/4+1/9+...1/N^2

This is the Java Program to Find the Sum of the Series 1/1+1/4+1/9+…1/N².

Problem Description

Given a number n, write a java program to find the sum of the series 1/1+1/4+1/9+…1/N².

Problem Solution

Start a loop from 1 to n, and add the square of the reciprocal of the loop variable to the sum.

Program/Source Code

Here is the source code of the Java Program to Find the Sum of the Series 1/1+1/4+1/9+…1/N². The program is successfully compiled and tested using IDE IntelliJ Idea in Windows 7. The program output is also shown below.

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//Java Program to Find the Sum of the Series 1/1+1/4+1/9+...1/N^2

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import java.io.BufferedReader;
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import java.io.InputStreamReader;
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public class Series81 {
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    // Function to find the sum of the series

    public static void main(String[] args) {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

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        int n;
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        try{
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            System.out.println("Enter the number of terms in the series");

            n = Integer.parseInt(br.readLine());

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        }catch (Exception e){
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            System.out.println("An error occurred");

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            return;
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        }
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        double sum = 0;
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        double i;
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        for(i=1; i<=n;i++){
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            sum +=(1/(Math.pow(i,2)));
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        }
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        System.out.println("The sum is " + sum);

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    }
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}
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Program Explanation

In the function main(), firstly the variable n is entered, then the loop for(i=1; i<=n;i++), is used to sum the squares of the reciprocal of the loop variable.

Time Complexity: O(n).

Runtime Test Cases

 
Case 1 (Simple Test Case):
 
Enter the number of terms in the series
34
The sum is 1.6159505883765848

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