# Sum of all even numbers in range L and R

Given two integers L and R, the task is to find the sum of all even numbers in range L and R.

Examples:

```Input: L = 2, R = 5
Output: 6
2 + 4 = 6

Input: L = 3, R = 8
Output: 18
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Method-1: Iterate from L to R and sum all the even numbers in that range.

Method-2: Find the sum all the natural numbers from L to R and subtract the sum of odd natural numbers in range L to R from it.

Method-3:

• Find the sum of all even numbers up to R i.e. No. of even numbers up to R will be R/2.
• Find the sum of all even numbers up to L-1 i.e. No. of even numbers up to L-1 will be (L-1)/2.
• Then subtract sumUptoL from sumuptoR.

Sum of all even numbers up to any N will be:
R*(R+1) where R = N/2

Below is the implementation of the above approach:

## C++

 `// C++ program to print the sum ` `// of all even numbers in range L and R ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the sum of ` `// all natural numbers ` `int` `sumNatural(``int` `n) ` `{ ` `    ``int` `sum = (n * (n + 1)); ` `    ``return` `sum; ` `} ` ` `  `// Function to return sum ` `// of even numbers in range L and R ` `int` `sumEven(``int` `l, ``int` `r) ` `{ ` `    ``return` `sumNatural(r/2) - sumNatural((l-1) / 2); ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `l = 2, r = 5; ` `    ``cout << ``"Sum of Natural numbers from L to R is "` `         ``<< sumEven(l, r); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to print the sum  ` `// of all even numbers in range L and R  ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `// Function to return the sum of  ` `// all natural numbers  ` `static` `int` `sumNatural(``int` `n)  ` `{  ` `    ``int` `sum = (n * (n + ``1``));  ` `    ``return` `sum;  ` `}  ` ` `  `// Function to return sum  ` `// of even numbers in range L and R  ` `static` `int` `sumEven(``int` `l, ``int` `r)  ` `{  ` `    ``return` `sumNatural(r/``2``) - sumNatural((l-``1``) / ``2``);  ` `}  ` ` `  `// Driver Code  ` `     `  `    ``public` `static` `void` `main (String[] args) { ` ` `  `        ``int` `l = ``2``, r = ``5``;  ` `        ``System.out.println (``"Sum of Natural numbers from L to R is "``+ ` `         ``sumEven(l, r));  ` `    ``} ` `} `

## Python3

 `# Python 3 program to print the sum  ` `# of all even numbers in range L and R  ` ` `  `# Function to return the sum   ` `# of all natural numbers  ` `def` `sumNatural(n): ` `    ``sum` `=` `(n ``*` `(n ``+` `1``)) ` `    ``return` `int``(``sum``) ` ` `  `# Function to return sum  ` `# of even numbers in range L and R  ` `def` `sumEven(l, r): ` `    ``return` `(sumNatural(``int``(r ``/` `2``)) ``-`  `            ``sumNatural(``int``((l ``-` `1``) ``/` `2``))) ` ` `  `# Driver Code  ` `l, r ``=` `2``, ``5` `print``(``"Sum of Natural numbers"``,  ` `             ``"from L to R is"``, sumEven(l, r))  ` ` `  `# This code is contributed  ` `# by 29AjayKumar `

## C#

 `// C# program to print the sum  ` `// of all even numbers in range L and R ` ` `  `using` `System; ` ` `  `public` `class` `GFG{ ` `         `  `// Function to return the sum of  ` `// all natural numbers  ` `static` `int` `sumNatural(``int` `n)  ` `{  ` `    ``int` `sum = (n * (n + 1));  ` `    ``return` `sum;  ` `}  ` ` `  `// Function to return sum  ` `// of even numbers in range L and R  ` `static` `int` `sumEven(``int` `l, ``int` `r)  ` `{  ` `    ``return` `sumNatural(r/2) - sumNatural((l-1) / 2);  ` `}  ` ` `  `// Driver Code  ` `     `  `    ``static` `public` `void` `Main (){ ` `            ``int` `l = 2, r = 5;  ` `        ``Console.WriteLine(``"Sum of Natural numbers from L to R is "``+ ` `        ``sumEven(l, r));  ` `    ``} ` `} `

## PHP

 ` `

Output:

```Sum of Natural numbers from L to R is 6
```

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