Question

Using the limit comparison test, and the limit of 1/sqrt(n), show that the limit of 1/sqrt(n)ln(n) is divergent

Answer 1

Does the following converge or diverge? Give reason. \[\sum_{n=2}^{\infty}\frac{ 1 }{ \sqrt{n}\ln n }\]
This is in the limit comparison chapter. The answer in the back of the book says it diverges using the limit comparison test with \[\sum_{}^{}\frac{ 1 }{ n}\]

Answer 2

I would have thought it could converge since the denominator is increasing, and numerator stays constant, so i would've thought that it could converge to 0