Iterative Constructs in Java

Chapter 9

Iterative Constructs in Java

Class 10 - Logix Kips ICSE Computer Applications with BlueJ

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Java Program: Sum of Series 2ⁿ - 1

30(ix). Write a program in Java to find the sum of the given series:

      1 + 3 + 7 + 15 + 31 + ..... + (2²⁰ - 1)

public class SumSeriesPowerOf2Minus1
{
    public static void main(String args[]) {
 
        double sum = 0;
       
        for (int i = 1; i <= 20; i++) {
            double term = Math.pow(2,i) - 1;
            sum += term;
        }
           
        System.out.println("Sum = " + sum);
       
    }
}
 

Sample Output
Sum = 2097130.0

📝 Explanation

1. First term = 1
2. Next term formula: term = 2 * term + 1
• 1 → 3 → 7 → 15 → 31 → 63 → 127 → 255 → …
3. Loop until term <= 20
4. Add each term to sum