(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

##\sum _{n=2}\dfrac {\left( -1\right) ^{n}} {\left( \ln n\right) ^{n}}##

3. The attempt at a solution

I have applied the Alternating Series test and it shows that it is convergent. However, I need to show that it's either absolute conv. or conditionally conv.

Next, I tried the root test:

##\lim _{n\rightarrow \infty }\sqrt {\left| \left( \dfrac {1} {\ln n}\right) ^{n}\right| }##, **Correction; this is the root of n**

Now, I'm tempted to use direct comparison with 1/n harmonic series and show divergence. However, I don't know, if I am allowed to do this since the root test tells me that then I have to find the limit of my An and classify it accordingly.

According to the root test:

if the limit >1 or infinity it diverges

if the limit <1 it converges absolutely.

if the limit =1 it's inconclusive.

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# Homework Help: Absolute Convergent, Conditionally Convergent?

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