# Sum of all subsets of a set formed by first n natural numbers

Given a number n, we need to find the sum of all the elements from all possible subsets of a set formed by first n natural numbers.

**Examples :**

Input : n = 2 Output : 6 Possible subsets are {{1}, {2}, {1, 2}}. Sum of elements in subsets is 1 + 2 + 1 + 2 = 6 Input : n = 3 Output : 24 Possible subsets are {{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} Sum of subsets is : 1 + 2 + 3 + (1 + 2) + (1 + 3) + (2 + 3) + (1 + 2 + 3)

A **simple solution** is to generate all subsets. For every subset, compute its sum and finally return overall sum.

An **efficient solution** is based on the fact that every number from 1 to n appears exactly 2^{(n-1)} times. So our required sum is (1 + 2 + 3 + ..+ n) * 2^{(n-1)}. The sum can be written as (n * (n + 1)/2) * 2^{(n-1)}

## C++

`// CPP program to find sum of all subsets ` `// of a set. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `unsigned ` `long` `long` `findSumSubsets(` `int` `n) ` `{ ` ` ` `// sum of subsets is (n * (n + 1) / 2) * ` ` ` `// pow(2, n-1) ` ` ` `return` `(n * (n + 1) / 2) * (1 << (n - 1)); ` `} ` ` ` `int` `main() ` `{ ` ` ` `int` `n = 3; ` ` ` `cout << findSumSubsets(n); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find sum of all subsets ` `// of a set. ` ` ` `class` `GFG { ` ` ` `static` `long` `findSumSubsets(` `int` `n) ` ` ` `{ ` ` ` `// sum of subsets is (n * (n + 1) / 2) * ` ` ` `// pow(2, n-1) ` ` ` `return` `(n * (n + ` `1` `) / ` `2` `) * (` `1` `<< (n - ` `1` `)); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `int` `n = ` `3` `; ` ` ` `System.out.print(findSumSubsets(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by Anant Agarwal. ` |

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## Python3

`# Python program to find ` `# sum of all subsets ` `# of a set. ` ` ` `def` `findSumSubsets( n): ` ` ` ` ` `# sum of subsets ` ` ` `# is (n * (n + 1) / 2) * ` ` ` `# pow(2, n-1) ` ` ` `return` `(n ` `*` `(n ` `+` `1` `) ` `/` `2` `) ` `*` `(` `1` `<< (n ` `-` `1` `)) ` ` ` `# Driver code ` `n ` `=` `3` `print` `(findSumSubsets(n)) ` ` ` `# This code is contributed ` `# by sunnysingh. ` |

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## C#

`// C# program to find sum of all subsets ` `// of a set. ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `static` `long` `findSumSubsets(` `int` `n) ` ` ` `{ ` ` ` ` ` `// sum of subsets is (n * (n + 1) / 2) * ` ` ` `// pow(2, n-1) ` ` ` `return` `(n * (n + 1) / 2) * (1 << (n - 1)); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `n = 3; ` ` ` ` ` `Console.WriteLine(findSumSubsets(n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by vt_m. ` |

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## PHP

`<?php ` `// PHP program to find sum ` `// of all subsets of a set ` ` ` `function` `findSumSubsets(` `$n` `) ` `{ ` ` ` `// sum of subsets is (n * ` ` ` `// (n + 1) / 2) * pow(2, n-1) ` ` ` `return` `(` `$n` `* (` `$n` `+ 1) / 2) * ` ` ` `(1 << (` `$n` `- 1)); ` `} ` ` ` `// Driver Code ` `$n` `= 3; ` `echo` `findSumSubsets(` `$n` `); ` ` ` `// This code is contributed by ajit ` `?> ` |

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**Output :**

24

This article is contributed by **Raj Kumar**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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