Is $\sum_{n=1}^{\infty}\frac{\arctan (n!)}{n^2}$ convergent or divergent?

Is $\sum_{n=1}^{\infty}\frac{\arctan (n!)}{n^2}$ convergent or divergent?

Which test should I use? I feel so dumb! 

Answer

Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.