Neka je
najmanja konstanta takva da, za sve realne brojeve
vrijedi:
Odredite cijeli broj najbliži broju 
.
Let
be the smallest constant such that for all real numbers
, the following inequality holds:
Determine the integer closest to .
[lang=hr]
Neka je $C$ najmanja konstanta takva da, za sve realne brojeve $a_1 \dots a_n$ vrijedi:
\[\sum_{i=1}^n \sum_{j=1}^n \frac{a_ia_j}{i+j} \le C \cdot \sum_{k=1}^n a_k^2\]
Odredite cijeli broj najbliži broju $10000C$.
[/lang]
[lang=en]
Let $C$ be the smallest constant such that for all real numbers $a_1 \dots a_n$, the following inequality holds:
\[\sum_{i=1}^n \sum_{j=1}^n \frac{a_ia_j}{i+j} \le C \cdot \sum_{k=1}^n a_k^2\]
Determine the integer closest to $10000C$.
[/lang]
