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Mathematics
Mathematics
Problem
For which real numbers
r
r
r
does the series
∑
n
=
3
∞
1
n
(
ln
n
)
[
ln
(
ln
n
)
]
r
\displaystyle \sum_{n=3}^{\infty} \frac{1}{n\,(\ln n)\,[\ln(\ln n)]^{r}}
n
=
3
∑
∞
n
(
ln
n
)
[
ln
(
ln
n
)
]
r
1
converge?
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