Let G(S) denote the sum of the elements of set S and F(n) be the sum of G(s) for all subsets of the set consisting of the first n natural numbers. For example, F(3) = (1) + (2) + (3) + (1 + 2) + (1 + 3) + (2 + 3) + (1 + 2 + 3) = 24. Given n, calculate F(1) + F(2) + ... + F(n).
Input:
1
2
3
Output:
1
7
31
How do i go about solving for an equation for sum of F(n) n = 1 to n.
I know the answer - but no idea how to arrive at it