JavaScript Program to Find Sum of N Natural Numbers

You can find the sum of n natural numbers in JavaScript using the formula sum = n * (n + 1) / 2 or by looping from 1 to n and adding each number.

Examples

Input5

Output15

Input10

Output55

Input1

Output1

How to Think About It

To find the sum of the first n natural numbers, think of adding all numbers from 1 up to n. You can do this by either adding each number one by one or using a simple math formula that calculates the total quickly without adding each number.

Algorithm

1

Get the input number n.

2

Use the formula sum = n * (n + 1) / 2 to calculate the sum.

3

Return or print the sum.

Code

javascript

function sumOfNaturalNumbers(n) {
  return n * (n + 1) / 2;
}

const n = 10;
console.log("Sum of", n, "natural numbers is", sumOfNaturalNumbers(n));

Output

Sum of 10 natural numbers is 55

Dry Run

Let's trace the example where n = 5 through the code.

1

Input value

n = 5

2

Apply formula

sum = 5 * (5 + 1) / 2 = 5 * 6 / 2 = 30 / 2 = 15

3

Return result

sum = 15

n	Calculation	Sum
5	5 * (5 + 1) / 2	15

Why This Works

Step 1: Why use the formula?

The formula n * (n + 1) / 2 quickly calculates the sum without needing to add each number one by one.

Step 2: How the formula works

It pairs numbers from start and end (like 1 and n) which always add up to the same total, then multiplies by half the count.

Step 3: Efficiency

Using the formula makes the program faster and simpler compared to looping through all numbers.

Alternative Approaches

Using a loop

javascript

function sumOfNaturalNumbersLoop(n) {
  let sum = 0;
  for (let i = 1; i <= n; i++) {
    sum += i;
  }
  return sum;
}

const n = 10;
console.log("Sum using loop:", sumOfNaturalNumbersLoop(n));

This method is easy to understand but slower for large n because it adds each number one by one.

Using recursion

javascript

function sumOfNaturalNumbersRec(n) {
  if (n === 1) return 1;
  return n + sumOfNaturalNumbersRec(n - 1);
}

const n = 10;
console.log("Sum using recursion:", sumOfNaturalNumbersRec(n));

Recursion is elegant but can cause stack overflow for very large n and is less efficient than the formula.

Complexity: O(1) time, O(1) space

Time Complexity

Using the formula takes constant time because it performs a fixed number of operations regardless of n.

Space Complexity

The formula uses constant space since it only stores a few variables.

Which Approach is Fastest?

The formula approach is fastest and most efficient compared to looping or recursion, which take O(n) time.

Approach	Time	Space	Best For
Formula	O(1)	O(1)	Fastest for any n
Loop	O(n)	O(1)	Easy to understand, small n
Recursion	O(n)	O(n)	Learning recursion, small n