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++

[sourcecode language=”CPP”]

// 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;

}

[/sourcecode]

## Java

[sourcecode language=”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.

[/sourcecode]

## Python3

[sourcecode language=”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.

[/sourcecode]

## C#

[sourcecode language=”CSHARP”]

// 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.

[/sourcecode]

## PHP

[sourcecode language=”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

?>

[/sourcecode]

**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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