series-concept question

**buttonbear** · March 22nd 2009, 05:54 PM

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?

**CaptainBlack** · March 23rd 2009, 02:38 PM

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

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