Java Program to Calculate the Sum of Natural Numbers

Introduction

The concept of calculating the sum of natural numbers is a fundamental exercise in mathematics and programming. It involves adding up all numbers from 1 to a given number n. In Java, this can be achieved through various methods, including loops and mathematical formulas.

In this article, you will learn how to calculate the sum of natural numbers in Java using different approaches. Explore practical examples that demonstrate the use of loops and the direct formula method to understand which scenarios each approach might be best suited for.

Using Loops to Calculate the Sum

Sum with a For Loop

1. Initialize a variable to hold the sum.

2. Use a for loop to iterate from 1 through n.

3. Add each number to the sum during each iteration.

   JAVA

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   public class SumNatural {
       public static void main(String[] args) {
           int n = 100;  // Example number
           int sum = 0;
   
           for (int i = 1; i <= n; i++) {
               sum += i;
           }
   
           System.out.println("Sum = " + sum);
       }
   }

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   This program initializes sum to 0 and increments it by each number from 1 to n (100 in this case). Finally, it prints the total sum.

Sum with a While Loop

1. Initialize the sum and a counter variable.

2. Use a while loop to add numbers until the counter exceeds n.

   JAVA

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   public class SumNatural {
       public static void main(String[] args) {
           int n = 100;
           int sum = 0;
           int i = 1;
   
           while (i <= n) {
               sum += i;
               i++;
           }
   
           System.out.println("Sum = " + sum);
       }
   }

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   In this snippet, sum is increased by i which is incremented in each iteration of the loop until i is greater than n.

Using the Formula Method

Direct Calculation Using the Formula

1. Apply the mathematical formula for the sum of the first n natural numbers: n(n + 1)/2.

   JAVA

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   public class SumNatural {
       public static void main(String[] args) {
           int n = 100;
           int sum = n * (n + 1) / 2;
   
           System.out.println("Sum = " + sum);
       }
   }

   Explain Code

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   The formula n(n + 1)/2 is a direct and efficient way to calculate the sum without looping. This method is extremely efficient for large values of n as it reduces the time complexity to O(1).

Conclusion

Calculating the sum of natural numbers can be done efficiently using different approaches in Java. Whether using iterative loops such as for and while, or applying a direct mathematical formula, each method has its suitability depending on the scenario and performance requirements. Start with loops for more comprehensive tasks that require iteration through each number, and use the formula for quick calculations that require minimal processing of individual elements. By mastering these techniques, develop robust solutions for a range of problems involving numeric calculations in Java.