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In which position of this sequence is 2005/ 2004 ?

Source: 2005 Bosnia & Herzegovina JBMO TST p3

May 27, 2020
Sequencealgebra

Problem Statement

Rational numbers are written in the following sequence: 11,21,12,31,22,13,41,32,23,14,...\frac{1}{1},\frac{2}{1},\frac{1}{2},\frac{3}{1},\frac{2}{2},\frac{1}{3},\frac{4}{1},\frac{3}{2},\frac{2}{3},\frac{1}{4}, . . . In which position of this sequence is 20052004\frac{2005}{2004} ?
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