Question

show that the series is divergent

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Answer 1

I know we need to use comparison test

Answer 2

that would be a good way to do it

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

when I show ln(n)/(n+1) is div.

I just use the fact that
ln(n)/(n+1) >1/(n+1)

Answer 7

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

Answer 8

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

for all \(n\ge16\)

Answer 9

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