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ERIZ · Answer 1 · 2018-06-25T01:51:47+0000

If you mean, "does the sequence
$a_n=\arctan(5n)$ converge", then yes, since
$\lim\limits_(n\to\infty)\arctan n=\frac\pi2$ .

If you mean, "does the series
$\sum\limits_n\arctan(5n)$ converge", then no, for the reason above (the summand passes the nth limit test for divergence, so the series diverges).

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