Question 3
Let $a,b,c$ be positive numbers. Define sequences $\{a_n\},\{b_n\},\{c_n\}$ by $a_0=a$, $b_0=b$, $c_0=c$, and
$$a_{n+1}=a_n+\frac2{b_n+c_n},\quad b_{n+1}=\frac2{c_n+a_n},\quad c_{n+1}=c_n+\frac2{a_n+b_n}$$
for every $n\in\mathbb Z_+$. Prove that $a_n$ tends to infinity as $n$ tends to infinity.
$$a_{n+1}=a_n+\frac2{b_n+c_n},\quad b_{n+1}=\frac2{c_n+a_n},\quad c_{n+1}=c_n+\frac2{a_n+b_n}$$
for every $n\in\mathbb Z_+$. Prove that $a_n$ tends to infinity as $n$ tends to infinity.