# 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 = 5Output:6 2 + 4 = 6Input: L = 3, R = 8Output:18

**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 <bits/stdc++.h> ` `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; ` `} ` |

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## 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)); ` ` ` `} ` `} ` |

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## 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 ` |

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## 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)); ` ` ` `} ` `} ` |

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## PHP

`<?php ` `// PHP program to print the sum of ` `// all even numbers in range L and R ` ` ` `// Function to return the sum of ` `// all natural numbers ` `function` `sumNatural(` `$n` `) ` `{ ` ` ` `$sum` `= (` `$n` `* (` `$n` `+ 1)); ` ` ` `return` `$sum` `; ` `} ` ` ` `// Function to return sum of ` `// even numbers in range L and R ` `function` `sumEven(` `$l` `, ` `$r` `) ` `{ ` ` ` `return` `sumNatural((int)(` `$r` `/ 2)) - ` ` ` `sumNatural((int)((` `$l` `- 1) / 2)); ` `} ` ` ` `// Driver Code ` `$l` `= 2; ` `$r` `= 5; ` `echo` `"Sum of Natural numbers "` `. ` ` ` `"from L to R is "` `. sumEven(` `$l` `, ` `$r` `); ` ` ` `// This code is contributed ` `// by Akanksha Rai ` `?> ` |

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**Output:**

Sum of Natural numbers from L to R is 6

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