Suppose $\lim \frac{u_{n}}{v_{n}} = 1$, prove $\sum u_{n}$ is convergent if and only if $\sum v_{n}$ is convergent.
$\lim\limits_{n \to \infty} \frac{a_n}{b_n}=l$ ; Prove $\sum\limits_{k=1}^\infty a_k$ converges iff $\sum\limits_{k=1}^\infty b_k$ converges.