I'm having trouble solving this sequence problem: let $p,q $ be odd integers and $u_n$, $v_n$ be real sequences, such that $u_n+v_n \to 0$ and $u_n^p+v_n^q \rightarrow 0$ as $n \to \infty$.
Show that $u_n \rightarrow 0$ and $v_n \to 0$ as $n \to \infty$.