Does the series $\sum \sin(100n)$ converge?

Question

Does the following series converge?

$$\sum \sin(100n) = \sin(100) + \sin(200) + \dots$$

This is at least the third time this very question's been asked in the last day. — Timbuc, Nov 29 '14 at 12:43
In the last link amWhy put, the very first answer is very good and basic, imo. — Timbuc, Nov 29 '14 at 12:52

score 2 · Answer 1 · edited Nov 29 '14 at 13:01

2

The series doesn't converge since the limit $$\lim_{ n \to \infty}\sin(100n)\ne 0$$

edited Nov 29 '14 at 13:01

André Nicolas

answered Nov 29 '14 at 12:43

2

This may be way easier to state than to prove, in particular for a beginner. It is true, though. – Timbuc Nov 29 '14 at 12:53
Apologies about the minor edit. I have a touchscreen little computer, was upvoting and "missed." The vote could not be changed unless the answer was edited. – André Nicolas Nov 29 '14 at 13:04

1 Answers1