The integral test should work for the first...
Note that is a decreasing function for , so
.
Let so that .
When and when , so
.
Therefore and thus the series is convergent.
Hey all I got two convergence problems I am stuck on
1) Determine whether 1/(x((lnx)^2)) from 2 to infinity converges or diverges. I've thought about the integral test and the comparison test but I'm still stuck.
[IMG]file:///C:/Users/TYLER%7E1.HOM/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
[IMG]file:///C:/Users/TYLER%7E1.HOM/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
2) Determine whether (-1)^(n-1)*(n/((n^2)+1)) from 1 to infinity converges or diverges and if it converges what's its limit. I tried direct comparison but that broke down at n=4 so I'm not sure what to do know.
Thanks for any help