# Summation of Combinations

Algebra Level 4

Consider the multiplication of any two distinct integers chosen from 1 to 100 inclusive. Define set $$S$$ denote the set which contains all such numbers (not necessarily distinct).

What is the sum of all the numbers in set $$S$$?

Details and Assumptions:

• Order is irrelevant, $$(1,4)$$ and $$(4,1)$$ count as $$1$$ combination. Also, the integers chosen within a pair have to be unequal.

• You might want to use a calculator as the calculation is large.

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