MathDB
Miklos Schweitzer 1950_7

Source: first round of 1950

October 2, 2008
floor functionceiling functionalgebra proposedalgebra

Problem Statement

Let x x be an arbitrary real number in (0,1) (0,1). For every positive integer k k, let fk(x) f_k(x) be the number of points mx\in [k,k \plus{} 1) m \equal{} 1,2,... Show that the sequence f1(x)f2(x)⋯fn(x)n \sqrt [n]{f_1(x)f_2(x)\cdots f_n(x)} is convergent and find its limit.
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