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Write a program to compute the value of Euler’s number e, that is used as the base of natural logarithms. Use the following formula? e=1+1/1!+1/2!+1/3!………………1/n!
Below is a Java program that computes the value of Euler’s number using the provided formula:
e=1+1/1!+1/2!+1/3!………………1/n!
The program will prompt the user for the value of and then calculate up to the -th term.
import java.util.Scanner;
public class EulerNumber {
// Function to calculate factorial of a number
public static double factorial(int n) {
double fact = 1;
for (int i = 1; i <= n; i++) {
fact *= i;
}
return fact;
}
// Function to calculate Euler's number e up to n terms
public static double calculateE(int n) {
double e = 1.0;
for (int i = 1; i <= n; i++) {
e += 1.0 / factorial(i);
}
return e;
}
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
// Prompt the user to enter the number of terms
System.out.print("Enter the number of terms: ");
int n = scanner.nextInt();
// Calculate Euler's number e
double e = calculateE(n);
// Output the result
System.out.printf("The value of Euler's number e up to %d terms is: %.15f\n", n, e);
scanner.close();
}
}
Explanation:
- The program defines a
factorialmethod to compute the factorial of a given number. - The
calculateEmethod computes the value of using the given series formula. - In the
mainmethod, the program prompts the user to enter the number of terms . - It calls the
calculateEmethod to compute the value of up to terms. - Finally, it prints the calculated value of with a precision of 15 decimal places.
Sample Output:
Enter the number of terms: 10
The value of Euler's number e up to 10 terms is: 2.718281801146385
In this example, when the user inputs 10, the program calculates and outputs the value of as approximately 2.718281801146385.
