series-concept question

Printable View

• March 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.

i'm not really sure where to start..please help?
• March 23rd 2009, 03:38 PM
CaptainBlack
Quote:

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