IMO Shortlist 1984 problem 19


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2. travnja 2012.
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The harmonic table is a triangular array:

1

\frac 12 \qquad \frac 12

\frac 13 \qquad \frac 16 \qquad \frac 13

\frac 14 \qquad \frac 1{12} \qquad \frac 1{12} \qquad \frac 14

Where a_{n,1} = \frac 1n and a_{n,k+1} = a_{n-1,k} - a_{n,k} for 1 \leq k \leq n-1. Find the harmonic mean of the 1985^{th} row.
Izvor: Međunarodna matematička olimpijada, shortlist 1984