Series Convergence Tests

Question

Which of the following is true about the series $$\displaystyle\sum_{n=2}^{\infty} \frac{1}{n \ln n}$$?

Accepted Answer

The series can be shown to diverge by the integral test.

Answer

The series can be shown to converge by limit comparison with $$\displaystyle\sum_{n=2}^{\infty} \frac{1}{n^{3/2}}$$.

Answer

The series can be shown to converge by the ratio test.

Answer

The series can be shown to converge by direct comparison with $$\displaystyle\sum_{n=2}^{\infty} \frac{1}{n^2}$$.

Question Leaderboard