# Java Program to Find the Sum of the Series 1/1!+1/2!+1/3!+…1/N!

This is the Java Program to Find the Sum of the Series 1/1!+1/2!+1/3!+…1/N!.

Problem Description

Given a number n, write a Java Program to Find the Sum of the Series 1/1!+1/2!+1/3!+…1/N!.

Problem Solution

Start a loop from 1 to n, and add the factorial of the reciprocal of the loop variable to the sum.
The factorial of the loop variable can be calculated using a nested loop.

Program/Source Code

Here is the source code of the Java Program to Find the Sum of the series 1/1!+1/2!+1/3!+…1/N!. The program is successfully compiled and tested using IDE IntelliJ Idea in Windows 7. The program output is also shown below.

1. ` `
2. `//Java Program to Find the Sum of the series 1/1!+1/2!+1/3!+...1/N!`
3. ` `
4. `import java.io.BufferedReader;`
5. `import java.io.InputStreamReader;`
6. ` `
7. `public class Series82 {`
8. `    // Function to calculate and display the sum of the series.`
9. `    public static void main(String[] args) {`
10. `        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));`
11. `        int n;`
12. `        try{`
13. `            System.out.println("Enter the number of terms in the series");`
14. `            n = Integer.parseInt(br.readLine());`
15. `        }catch (Exception e){`
16. `            System.out.println("An error occurred");`
17. `            return;`
18. `        }`
19. `        double sum = 0;`
20. `        double i;`
21. `        int j;`
22. `        long fac;`
23. `        for(i=1; i<=n;i++){`
24. `            fac =1;`
25. `            for(j=2; j<=i;j++){`
26. `                fac*=j;`
27. `            }`
28. `            sum +=(1.0d/fac);`
29. `        }`
30. `        System.out.println("The sum is " + sum);`
31. `    }`
32. `}`
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 reciprocal of the factorial of the loop variable. The loop for(j=2; j<=i;j++) is used to calculate the factorial of i.

Time Complexity: O(n2).

Runtime Test Cases
```
Case 1 (Simple Test Case):

Enter the number of terms in the series
34
The sum is 1.7182818284590455```

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