Why is the series $a_n={1\over2^n+n}$ convergent whereas the series $a_n={3^n+1\over4^n+5}$ is absolutely convergent? Since both use the comparison test to the geometric series, what makes one abs. convergent and the other not? I know a series converges absolutely if $|a_n|$ converges so why the difference?
Asked
Active
Viewed 137 times
1 Answers
0
A series that is positive is absolutely convergent as soon as it is convergent. So both are absolutely convergent.
vinnief
- 215
-
Thank you. That's what I thought.. – user71865 Apr 10 '13 at 15:51
-
(That's what I thought) vs (what makes one abs. convergent and the other not?) – Did Apr 10 '13 at 16:00