Suppose $\sum_{n>1} a_n=\infty$ and $0
Let $b_k=a_k$ or $b_k=0$ for all integers $k$.
Let $R=\lim_{n\rightarrow\infty}((1/n)\sum_{q=1}^{q=n} b_q/a_q)$
If $R>0$, how to show that $\sum_{n>1}b_n=\infty$?
If $0<\lim_{n\rightarrow\infty}((1/\sqrt n)\sum_{q=1}^{q=n} b_q/a_q)$, must $\sum_{n>1}b_n=\infty$?