(Solved): please help (12 points) Determine if each series converges or diverges: (Justify why) a) \( \sum_{n= ...

(12 points) Determine if each series converges or diverges: (Justify why) a) \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{\sqrt{n}} \) b) \( \sum_{n=1}^{\infty} \tan ^{-1} n \) c) \( \sum_{n=1}^{\infty} \frac{n\left(5^{n}\right)}{6^{n}} \) For parts a and b, use whatever test you think is appropriate. For part c, use the ratio test.