John computes the sum of the elements of each of the 15 two-element subsets of
{1,2,3,4,5,6}.
What is the sum of these 15 sums?
15 two-element subsets:
1,2,3,4,5,61,22,33,44,55,61,32,43,54,61,42,53,61,52,61,6
the numbers are: 5×1+5×2+5×3+5×4+5×5+5×6=5×(1+2+3+4+5+6)=5×(1+62)×6=5×(72)×6=105=(n−1)×(1+n2)×n=3×(n+13)
