Is sum[n=1,infty][(-1)^n ln(n)/n] divergent or convergent? Justify.

[forever_not_in_use]

I have to figure out if the series is divergent or convergent, and justify my answer. Here is the series:

. . . . .\(\displaystyle \displaystyle \sum_{n=1}^{\infty}\, \dfrac{ (-1)^n \, \cdot\, \ln(n) }{n}\)

I'm having trouble figuring out what method to use. I have tried the alternating series test but it does not fit the parameters, and the ratio test also doesn't work. Any ideas? Thank you.

 

[tkhunny]

Please show your work on the Alternating Series Test.