3

Part of 2000 Italy TST

Problems(1)

sequence bounding

Source: Italy TST 2000

Given positive numbers

a_1

b_1

, consider the sequences defined by a_{n+1}=a_n+\frac{1}{b_n}, b_{n+1}=b_n+\frac{1}{a_n} (n \ge 1) Prove that

a_{25}+b_{25} \geq 10\sqrt{2}

inductionalgebra unsolvedalgebra