Problem A. 661. (January 2016)

A. 661. Let \(\displaystyle K\) be a fixed positive integer. Let \(\displaystyle (a_0,a_1,\dots)\) be the sequence of real numbers that satisfies \(\displaystyle a_0=-1\) and

\(\displaystyle \sum_{\substack{i_0,i_1,\dots,i_K\ge0 \\ i_0+i_1+\dots+i_K=n}} \frac{a_{i_1}\cdot\dots\cdot a_{i_K}}{i_0+1} =0 \)

for every positive integer \(\displaystyle n\). Show that \(\displaystyle a_n>0\) for \(\displaystyle n\ge1\).

(5 pont)

Deadline expired on February 10, 2016.

Statistics:

1 student sent a solution.
5 points:	Williams Kada.

Problems in Mathematics of KöMaL, January 2016