IMO Shortlist 1984 problem 19
Dodao/la:
arhiva2. travnja 2012. The harmonic table is a triangular array:
![\frac 14 \qquad \frac 1{12} \qquad \frac 1{12} \qquad \frac 14](/media/m/e/6/7/e6739203009b9a7296732f26900c10bb.png)
Where
![a_{n,1} = \frac 1n](/media/m/e/5/3/e5336f7988a7f74a076ae3dee6a213ec.png)
and
![a_{n,k+1} = a_{n-1,k} - a_{n,k}](/media/m/3/f/f/3ff2d8e2eef2904e0d56c9ced8ca62a5.png)
for
![1 \leq k \leq n-1.](/media/m/f/e/4/fe421039da0e66c7601b20b89540635f.png)
Find the harmonic mean of the
![1985^{th}](/media/m/a/2/c/a2c0c7162b441722a45eeed0a29848db.png)
row.
%V0
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