# series-concept question

• Mar 22nd 2009, 06:54 PM
buttonbear
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.

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.
$a_n=1/n^2$ and $b_n=n$