Me and my friend are debating on wether the follow seris is convergent or divergent. The seris is the sum of (-1)^n-1 * ln(n)/n.
p test and comparision tests.
And alternating series test
The Attempt at a Solution
My approach to this problem was that the ln(n) portion grows much slower than n portion. So I compared this function to 1/n. I know 1/n is divergent, so I concluded the above function was also divergent. My friend argues that the limit of ln (n)/n is zero and is greater than ln(n+1)/(n+1). So he says its convergent.