Which of the following statements about convergence of the series \(\displaystyle \sum_{n=1}^\infty \frac{1}{\ln(n+1)} \) is true?

\(\displaystyle \frac{1}{\ln(n+1)} \) is greater than \(\displaystyle \frac{1}{n} \) for all values of \(n\geq 1\).

Since \(\displaystyle \sum_{n=1}^\infty \frac{1}{n} \) is a \(p\)-series that diverges, \(\displaystyle \sum_{n=1}^\infty \frac{1}{\ln(n+1)} \) must also diverge.