does sum[n=1,infty][arctan(n)/(1+n^2)] converge or diverge? Which test to use?

[Catherine Xia]

The question is determine whether the series converges or diverges, and to name the test used. The series is:

. . . . .\(\displaystyle \displaystyle \sum_{n=1}^{\infty}\, \dfrac{\arctan(n)}{1\, +\, n^2}\)

I used the Integral Test and found that it converges. but on the answer sheet it says "Limit Comparison Test" and that is the only correct answer. Was I wrong or was the answer key wrong?

 

[tkhunny]

How about a third choice? Read my signature, below.

Integral Test
Comparison Test
Limit Comparison Test
Are there others?

Now, if you were just discussing the Limit Comparison Test, in class, you may have wanted to try that, first.