# Sum of all odd natural numbers in range L and R

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 ` `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#

 `// 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

 ` `

Output:

```Sum of odd natural numbers from L to R is 8
```

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