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Tags: induction, algebra unsolved, algebra



We denote $N_{2010}=\{1,2,\cdots,2010\}$ (a)How many non empty subsets does this set have? (b)For every non empty subset of the set $N_{2010}$ we take the product of the elements of the subset. What is the sum of these products? (c)Same question as the (b) part for the set $-N_{2010}=\{-1,-2,\cdots,-2010\}$. Albanian National Mathematical Olympiad 2010---12 GRADE Question 2.