00:01
In this question, we're going to determine the convergence or divergence of the series summed from n equals 1 to infinity of the arc tangent of 2n.
00:11
Now, if i look at my answer choices, i realize that we're interested in the nth term test and the integral test in this question.
00:21
Now, the nth term test is a test for divergence only.
00:28
So therefore, answer choice a makes no sense.
00:33
Nothing can ever converge by the nth term test.
00:38
So let's run through the nth term test.
00:41
The nth term test says i should look at the limit as n approaches infinity of my general term.
00:49
In this case, the limit as n approaches infinity of the arc tangent of 2n.
00:56
To evaluate this limit, we imagine plugging in as n approaches infinity, 2n approaches infinity as well.
01:07
So we are taking the arc tangent of something approaching infinity.
01:12
When you take the arc tangent of something very, very large, the result gets very close to pi over 2.
01:22
This result gets very, very close to pi over 2.
01:26
Now, what's important about that? for our purposes, it's important that that's not 0...