MathDB
Sum of all elements of a set

Source: Moldova TST 2011, day 2, problem 1

March 8, 2011
arithmetic sequencenumber theory unsolvednumber theory

Problem Statement

Natural numbers have been divided in groups as follow: (1),(2,4),(3,5,7),(6,8,10,12),(9,11,13,15,17),…(1), (2, 4), (3, 5, 7), (6, 8, 10, 12), (9, 11, 13, 15, 17), \ldots. Let SnS_n be the sum of the elements of the nnth group. Prove that S2n+12n+1−S2n2n\frac{S_{2n+1}}{2n+1}-\frac{S_{2n}}{2n} is even.
Back to ProblemsView on AoPS