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Bundeswettbewerb Mathematik 1980 Problem 1.4

Source: Bundeswettbewerb Mathematik 1980 Round 1

September 23, 2022
SequenceSumnumber theory

Problem Statement

Consider the sequence a1,a2,a3,…a_1, a_2, a_3, \ldots with an=1n(n+1). a_n = \frac{1}{n(n+1)}. In how many ways can the number 11980\frac{1}{1980} be represented as the sum of finitely many consecutive terms of this sequence?
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