## Calculus (3rd Edition)

The series $\sum_{n=1}^{\infty} \frac{1}{(\ln n)^4}$ diverges.
Since $\ln n\lt n^{1/4}$, then $(\ln n)^4\lt n$ and hence $$\frac{1}{(\ln n)^4}\gt \frac{1}{n}.$$ Now, since the series $\sum_{n=1}^{\infty} \frac{1}{n}$ is a divergent p-series, then the series $\sum_{n=1}^{\infty} \frac{1}{(\ln n)^4}$ diverges.