W. 22

Problems(1)

Source: 2009 Jozse Wildt International Mathematical Competition

a_i >0

i=1, 2, \cdots , n

\left (\frac{a_1}{a_2} \right )^k + \left (\frac{a_2}{a_3} \right )^k + \cdots + \left (\frac{a_n}{a_1} \right )^k \geq \frac{a_1}{a_2}+\frac{a_2}{a_3}+\cdots + \frac{a_n}{a_1}

k\in \mathbb{N}