# Sum of all natural numbers in range L to R

Given a range L and R, the task is to find the sum of all natural numbers in range L to R.

**Examples**:

Input:L = 2, R = 5Output:14 2 + 3 + 4 + 5 = 14Input:L = 10, R = 20Output:165

A **naive approach **is to traverse from L to R and add all the elements one by one to get the sum.

An **efficient approach** is to use the formula for the sum of first N natural numbers. The idea of the inclusion-exclusion principle helps to solve the above problem. Find the sum of natural numbers till **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 <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; ` `} ` |

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## Java

`// 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 ` |

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## Python3

`# 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 ` |

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## 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 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 ` |

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## PHP

`<?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 ` `?> ` |

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**Output:**

Sum of Natural numbers from L to R is 14

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