Related Articles
Sum of all subsets of a set formed by first n natural numbers
• Difficulty Level : Medium
• Last Updated : 19 Mar, 2021

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 ``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;``}`

## 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.`

## 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.`

## 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.`

## PHP

 ``

## Javascript

 ``

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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up