 # JavaScript Program To Find Sum Of Odd Numbers Less Than N

In our previous tutorials you learnt how to write a JavaScript program to find sum of N numbers and sum of N even numbers. In this tutorial, you’ll learn how to write a JavaScript program to find sum of odd numbers less than N.

## Traditional Method To Find Sum Of Odd Numbers

Let’s first implement the solution to the above problem using traditional method. The program will iterate from 1 to N and check for number to be odd. If the number is odd, it’s added to the total sum.

Here is how the implement looks :

``````/*
** Method to check if a number is odd
*/
function odd(n){
return Boolean(n%2)
}

/*
** Method to find sum of odd numbers till n
*/
function findSum(n) {
let sum = 0;
for(let i = 0; i <= n; i++){
if(odd(i)) {
sum += i;
}
}
return sum
}

console.log(`sum is \${findSum(10)}`)``````

## Mathematical Approach To Find Sum Of Odd Numbers

The traditional method to find the sum of N odd numbers can be optimized using the mathematical approach.

To find the sum of N odd numbers :

sum = 1 + 3 + 5 + 7 + … + (2n – 1) – EQ-1

From EQ-1 :

sum = (2-1) + (6-1) + (8-1) + … + (2n-1)

sum = (2+6+8+ …. + 2n) – n

sum = n*n + n -n

sum = n*n

Now let’s try to implement the above formula to calculate sum of odd numbers less than N.

``````/*
** Method to check if a number is odd
*/
function odd(n){
return Boolean(n%2)
}

/*
** Method to find sum of odd numbers less num
*/
function findSumOddNumbers(num) {
let n = 0;
if(odd(num)){
n = (num - 1) / 2
} else {
n = num / 2
}
return n * n
}

console.log(`Sum is \${findSumOddNumbers(50)}`);``````

## Wrapping It Up

In this tutorial, you learnt how to find the sum of odd numbers less than N using the traditional method and mathematical method. Do let us know your thoughts in the comments below.