IMO 1984 - Shortlisted Problems Question 19

(CAN 5) The triangular array $(a_{n,k})$ of numbers is given by $a_{n,1}=1/n$, for $n=1,2,\ldots$, $a_{n,k+1}=a_{n-1,k}-a_{n,k}$, for $1\le k\le n-1$. Find the harmonic mean of the 1985th row.