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Does arctan(5n) converge or diverge?

User Alfietap
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1 Answer

7 votes
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).
User ERIZ
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