Suma de todos los números naturales en el rango L a R

Dado un rango L y R, la tarea es encontrar la suma de todos los números naturales en el rango L a R. 
Ejemplos : 
 

Input: L = 2, R = 5
Output: 14
2 + 3 + 4 + 5 = 14

Input: L = 10, R = 20
Output: 165

Un enfoque ingenuo es atravesar de L a R y sumar todos los elementos uno por uno para obtener la suma.
Un enfoque eficiente es usar la fórmula para la suma de los primeros N números naturales . La idea del principio de inclusión-exclusión ayuda a resolver el problema anterior. Encuentre la suma de los números naturales hasta R y L-1 y luego reste sum(R)-sum(l-1) .
A continuación se muestra la implementación del enfoque anterior: 
 

// 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 natural numbers
int sumNatural(int n)
{
    int sum = (n * (n + 1)) / 2;
    return sum;
}
 
// Function to return the sum
// of all numbers in range L and R
int suminRange(int l, int r)
{
    return sumNatural(r) - sumNatural(l - 1);
}
 
// Driver Code
int main()
{
    int l = 2, r = 5;
    cout << "Sum of Natural numbers from L to R is "
         << suminRange(l, r);
 
    return 0;
}

// Java program to print the sum
// of all numbers in range L and R
 
class GFG{
// Function to return the sum of
// all natural numbers
static int sumNatural(int n)
{
    int sum = (n * (n + 1)) / 2;
    return sum;
}
 
// Function to return the sum
// of all numbers in range L and R
static int suminRange(int l, int r)
{
    return sumNatural(r) - sumNatural(l - 1);
}
 
// 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 "+suminRange(l, r));
 
}
}
// This code is contributed by mits

# Python3 program to print the sum  of
# all numbers in range L and R
 
# Function to return the sum of all natural numbers
def sumNatural(n):
 
    sum = (n*(n+1))//2
 
    return sum
 
# Function to return the sum
# of all numbers in range L and R
def suminRange(l, r):
    return sumNatural(r) - sumNatural(l-1)
 
#  Driver Code
l =2; r= 5
print("Sum of Natural numbers 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 natural numbers
static int sumNatural(int n)
{
    int sum = (n * (n + 1)) / 2;
    return sum;
}
 
// Function to return the sum
// of all numbers in range L and R
static int suminRange(int l, int r)
{
    return sumNatural(r) -
           sumNatural(l - 1);
}
 
// Driver Code
static public void Main ()
{
    int l = 2, r = 5;
    Console.WriteLine("Sum of Natural numbers " +
                              "from L to R is " +
                               suminRange(l, r));
}
}
 
// This code is contributed by akt_mit

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

<script>
// JavaScript program to print the sum
// of all numbers in range L and R
 
// Function to return the sum of
// all natural numbers
function sumNatural(n)
{
    sum = (n * (n + 1)) / 2;
    return sum;
}
 
// Function to return the sum
// of all numbers in range L and R
function suminRange(l, r)
{
    return sumNatural(r) -
           sumNatural(l - 1);
}
 
// Driver Code
let l = 2;
let r = 5;
document.write("Sum of Natural numbers from L to R is "+
             suminRange(l, r));
 
// This code is contributed by sravan kumar gottumukkalan
 
</script>

Sum of Natural numbers from L to R is 14

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)