5. (16 points) Determine whether the series listed below are divergent, absolutely convergent (hence convergent), or conditionally convergent. Indicate the tests or result you apply to support your conclusion. \text

{ a. } \sum_{n=1}^{\infty} \frac{(-1)^{n-1} e^{1 / n}}{n} \text { b. } \sum_{n=1}^{\infty} \frac{1}{n+n \tan ^{-1} n} \text { c. } \sum_{n=1}^{\infty} \frac{n !}{\ln n} \text { d. } \sum_{n=1}^{\infty} \frac{(-n)^{3}+1}{7^{n}}