I'm having trouble trying to figure out what to do for convergence and divergence for a series that has lnx in it

for example

and

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- Apr 21st 2008, 01:53 PMakhayoonsums with lnx
I'm having trouble trying to figure out what to do for convergence and divergence for a series that has lnx in it

for example

and - Apr 21st 2008, 02:00 PMJhevon
- Apr 21st 2008, 02:01 PMMoo
Hello,

I think ratio test can work too... - Apr 21st 2008, 02:02 PMMathstud28
- Apr 21st 2008, 02:09 PMJhevon
- Apr 21st 2008, 02:12 PMMathstud28
- Apr 21st 2008, 02:13 PMJhevon
- Apr 21st 2008, 02:52 PMPlato

Simple comparison with p-series. - Apr 21st 2008, 03:00 PMakhayoon
I don't understand how that comparison works...I mean where did the come from and how did it become to the exponent 3/2?? so confused (Doh)

- Apr 21st 2008, 03:02 PMMathstud28
- Apr 21st 2008, 03:03 PMakhayoon
so that was completely arbitrary and u could've essentially picked anything greater than lnx??

- Apr 21st 2008, 03:03 PMJhevon
- Apr 21st 2008, 05:51 PMakhayoon
well how would you even integrate

by parts? - Apr 21st 2008, 06:00 PMMathstud28
- Apr 21st 2008, 06:06 PMakhayoon

so the book is telling me to use the ratio test...

and you get

so now I guess how would ln(k+1)/lnk go to 1 would be my basic question...

all I know is is that ln(n)/n goes to 0 as n goes to infinity but i haven't seem something like this before..