Hello
Determine whether the following series is convergent or divergent:
$\displaystyle \displaystyle \sum_{n=2}^{\infty} \dfrac{1}{ln^e(n)}$
This one makes me crazy!
How to deal with it ?!
The power e is on the whole ln.
I may be being a bit dense here, but what does the notation $\displaystyle \ln^e(n)$ denote? Is this a fractionally iterated logarithm, a fractional derivative (not likely I would have thought), abused notation for $\displaystyle (\ln(n))^e$, ... ?
By the way as $\displaystyle \ln(n)$ grows more slowly than any positive power of $\displaystyle $$n$, so does $\displaystyle (\ln(n))^e$ and in particular for $\displaystyle $$n$ large enough there exists a $\displaystyle $$k$ such that $\displaystyle (\ln(n))^e<k\times n$, and so the series diverges.
CB