Sum of all odd natural numbers in range L and R

Last Updated : 11 Jul, 2025

Given two integers L and R, the task is to find the sum of all odd natural numbers in range L and R inclusive.
Examples:

Input: L = 2, R = 5
Output: 8
3 + 5 = 8

Input: L = 7, R = 13
Output: 40

A naive approach is to traverse from L to R and summate the elements to get the answer.
An efficient approach is to use the formula for calculating the sum of all odd natural numbers upto R and L-1 and then subtract sum(R)-sum(L-1).
Below is the implementation of the above approach:

C++

// C++ program to print the sum
// of all numbers in range L and R
#include <bits/stdc++.h>
using namespace std;

// Function to return the sum of
// all odd natural numbers
int sumOdd(int n)
{
    int terms = (n + 1) / 2;
    int sum = terms * terms;
    return sum;
}

// Function to return the sum
// of all odd numbers in range L and R
int suminRange(int l, int r)
{
    return sumOdd(r) - sumOdd(l - 1);
}

// Driver Code
int main()
{
    int l = 2, r = 5;
    cout << "Sum of odd natural numbers from L to R is "
         << suminRange(l, r);

    return 0;
}

Java

 // Java program to print the sum
// of all numbers in range L and R

import java.io.*;

class GFG {
   


// Function to return the sum of
// all odd natural numbers
static int sumOdd(int n)
{
    int terms = (n + 1) / 2;
    int sum = terms * terms;
    return sum;
}

// Function to return the sum
// of all odd numbers in range L and R
static int suminRange(int l, int r)
{
    return sumOdd(r) - sumOdd(l - 1);
}

// Driver Code
public static void main (String[] args) {
            int l = 2, r = 5;
    System.out.print( "Sum of odd natural numbers from L to R is "
        + suminRange(l, r));
    }
}
// This code is contributed by shs..

Python3

# Python 3 program to print the sum 
# of all numbers in range L and R 

# Function to return the sum of 
# all odd natural numbers 
def sumOdd(n):
    terms = (n + 1)//2
    sum1 = terms * terms
    return sum1

# Function to return the sum 
# of all odd numbers in range L and R 
def suminRange(l, r):
    return sumOdd(r) - sumOdd(l - 1)
    
# Driver code
l = 2; r = 5
print("Sum of odd natural number",
      "from L to R is", suminRange(l, r))

# This code is contributed by Shrikant13

// C# program to print the sum
// of all numbers in range L and R
using System;

class GFG 
{
    
// Function to return the sum of
// all odd natural numbers
static int sumOdd(int n)
{
    int terms = (n + 1) / 2;
    int sum = terms * terms;
    return sum;
}

// Function to return the sum
// of all odd numbers in range L and R
static int suminRange(int l, int r)
{
    return sumOdd(r) - sumOdd(l - 1);
}

// Driver Code
public static void Main () 
{
    int l = 2, r = 5;
    Console.WriteLine( "Sum of odd natural numbers " + 
                "from L to R is " + suminRange(l, r));
}
}

// This code is contributed by shs..

PHP

<?php
//PHP program to print the sum 
// of all numbers in range L and R 
// Function to return the sum of 
// all odd natural numbers 
function sumOdd($n) 
{ 
    $terms = (int)($n + 1) / 2; 
    $sum = $terms * $terms; 
    return $sum; 
} 

// Function to return the sum 
// of all odd numbers in range L and R 
function  suminRange($l, $r) 
{ 
    return sumOdd($r) - sumOdd($l - 1); 
} 

// Driver Code 

    $l = 2;
    $r = 5; 
    echo "Sum of odd natural numbers from L to R is ",
         suminRange($l, $r); 

?>

JavaScript

<script>

//JavaScript program to print the sum
// of all numbers in range L and R

// Function to return the sum of
// all odd natural numbers
function sumOdd(n)
{
    terms = (n + 1) / 2;
    sum = terms * terms;
    return sum;
}

// Function to return the sum
// of all odd numbers in range L and R
function suminRange(l, r)
{
    return sumOdd(r) - sumOdd(l - 1);
}

// Driver Code

let    l = 2;
let    r = 5;
    document.write("Sum of odd natural numbers from L to R is "+
        suminRange(l, r));
        
// This code is contributed by sravan kumar

</script>

Output:

Sum of odd natural numbers from L to R is 8

Time Complexity: O(1)

Auxiliary Space: O(1), since no extra space has been taken.

Analysis of Algorithms

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Sum of all odd natural numbers in range L and R

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