max> \sqrt{2005}

[Claudiu Mindrila]

Sirurile \( \left(a_{n}\right)_{n\ge0},\ \left(b_{n}\right)_{n\ge0} \) sunt definite prin relatiile \( a_{n+1}=a_{n}+\frac{1}{2b_{n}},\ b_{n+1}=b_{n}+\frac{1}{2a_{n}} \) cu \( a_{0},\ b_{0}>0 \) date. Sa se demonstreze ca \( \max\left\{ a_{2004},\ b_{2004}\right\} >\sqrt{2005} \).

Dorin Marghidanu