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

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;
}

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

<?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
?>

Javascript

<script>

// Javascript 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)
{
    let sum = Math.floor(n * (n + 1));
    return sum;
}

// Function to return sum
// of even numbers in range L and R
function sumEven(l, r)
{
    return sumNatural(Math.floor(r/2)) - sumNatural(Math.floor(l-1) / 2);
}


// driver program

        let l = 2, r = 5;
        document.write ("Sum of Natural numbers from L to R is "+
         sumEven(l, r));

</script>

Output:

Sum of Natural numbers from L to R is 6

Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.