How do you determine whether the infinite sequence $a_n=arctan(2n)$ converges or diverges?

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Answer 1 · 2014-09-28T13:17:35

As shown in the graph below, $lim_{x to infty}arctanx=pi/2$ .

enter image source here

So, we will have the same limit value for

$lim_{n to infty}arctan(2n)=pi/2$ .

Hence, it converges.

How do you determine whether the infinite sequence a_n=arctan(2n)a_n=arctan(2n) converges or diverges?