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

Factorial of a number simply returns out the multiplication of that number with all numbers lesser than the number up to 1 over which factorial is applied. Now the question arises of whether the series is convergent or divergent. According to concepts of  Infinite series and factorial in mathematics, the series may not converge but it can contain a convergent subsequence.

Illustration:

n! = n * (n-1) × (n-2) × (n-3) × (n-4) × …… × 4 × 3 × 2 × 1

Input      : n = 5
Processing : 1/1! + 2/2! + 3/3! + 4/4! + 5/5!
             1    + 2/2  + 3/6  + 4/24 + 5/120
Output     : 2.708333333333333            

Approach : 

• Enter the number of terms N.
• Create a function to calculate the sum of series, say, calculateSum.
• In calculateSum function(), create a variable sum which stores the total sum of the series.
• Run a loop N times.
• Call factorial function() to calculate the factorial of a given number.
• Return sum.

Implementation:

Java

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

// Importing java generic libraries
import java.io.*;

class GFG {

    // Function(recursive) to calculate factorial
    public static double factorial(int i)
    {
        // Step1: Base case
        if (i == 1) {
            return 1;
        }
        // Step2&3: Recursion execution & call statements
        return i * factorial(i - 1);
    }

    // Function to calculate sum of series
    public static double calculateSum(int N)
    {
        // Store total_sum in sum
        double sum = 0;

        // Iteration by running a loop N times
        for (int i = 1; i <= N; i++) {
            sum = sum + ((double)i / factorial(i));
        }

        // Return calculated final sum
        return sum;
    }

    // Main driver method
    public static void main(String[] args)
    {
        /* No of terms in series
           taken inn order to show output */
        int N = 5;

        // Print sum of series by
        // calling function calculating sum of series
        System.out.println("The sum of series upto " + N
                           + " terms is : "
                           + calculateSum(N));
    }
}

Output

The sum of series upto 5 terms is : 2.708333333333333

Time Complexity: O(n)

Auxiliary Space: O(n) for call stack