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Mathematics 40 Online
OpenStudy (anonymous):

show that the series is divergent [URL=http://imageshack.us/photo/my-images/543/87173732.png/][IMG]http://imageshack.us/a/img543/8813/87173732.png[/IMG][/URL] Uploaded with [URL=http://imageshack.us]ImageShack.us[/URL]

OpenStudy (anonymous):

I know we need to use comparison test

OpenStudy (zarkon):

that would be a good way to do it

OpenStudy (anonymous):

I know how to show ln(n)/(n+1) is div.

OpenStudy (zarkon):

so what is the problem with ln(ln(n))

OpenStudy (zarkon):

\(\ln(\ln(n))>1\) for all \(n>N\) where \(N\) is some natural number

OpenStudy (anonymous):

when I show ln(n)/(n+1) is div. I just use the fact that ln(n)/(n+1) >1/(n+1)

OpenStudy (anonymous):

so I can use the same logic, I see know bottom boundary of series does not important

OpenStudy (zarkon):

\[\frac{\ln(\ln(n))}{n+1}>\frac{1}{n+1}\] for all \(n\ge16\)

OpenStudy (anonymous):

yes, that what I am looking for, thanks @zarkon (:

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