Prove/Disprove $\sum a_n$ and $\sum b_n$ converge together iff $\underset{n\to \infty }{\mathop{\lim }}\,{{a}_{n}/b_n } = 1$
True/False: $\mathop {\lim }\limits_{n \to \infty } {{{a_n}} \over {{b_n}}} = 1$ implies $\sum {{a_n},\sum {{b_n}} } $ converge or diverge together.