# Math Help - series-concept question

1. ## series-concept question

give an example of a pair of series $\sum_{}an$ and $\sum_{}bn$ with positive terms where $\lim_{n\to{\infty}}\frac{an}{bn}=0$ and $\sum_{}bn$ diverges, but $\sum_{}an$ converges.

i'm not really sure where to start..please help?

2. Originally Posted by buttonbear
give an example of a pair of series $\sum_{}an$ and $\sum_{}bn$ with positive terms where $\lim_{n\to{\infty}}\frac{an}{bn}=0$ and $\sum_{}bn$ diverges, but $\sum_{}an$ converges.

i'm not really sure where to start..please help?
$a_n=1/n^2$ and $b_n=n$

CB