Mathematics

Problem

For which of the following series is the

n

th-term test inconclusive, so that another convergence test is required? a)

\displaystyle\sum_{n=1}^{\infty}\frac{3n}{n+2}

\displaystyle\sum_{n=2}^{\infty}\frac{1}{n(\ln n)^{2}}

\displaystyle\sum_{n=1}^{\infty}\frac{(-1)^{n}(n+5)}{n}

\displaystyle\sum_{n=1}^{\infty}\frac{\ln n}{\ln(n+1)}