Which of the following tests Can determine the convergence/divergence of the series \sum_{n=2}^{\infty} \frac{1}{n \ln n} ?

Question

Which of the following tests Can determine the convergence/divergence of the series   \sum_{n=2}^{\infty} \frac{1}{n \ln n} ?

Accepted Answer

Integral test

Answer

Root test

Answer

Limit comparison test with   \sum_{n=1}^{\infty} \frac{1}{ n^2}

Answer

From the fact that   \sum_{n=1}^{\infty} |u_n|  converges   \Rightarrow \sum_{n=1}^{\infty} u_n  converges

Answer

Ratio test

Answer

From the fact that   \sum_{n=1}^{\infty} u_n  converges   \Rightarrow \lim_{n	o \infty}u_n=0

Answer

Direct comparison test with   \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}

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