The sequence S:=(sin n) is divergent.

Question

I've seen its proof in Bartle and Sherbert.

But, I think a lot more interesting proofs of this can be done. Plz, help me in writing its proof in other possible ways. So, that I can develop more constructive ideas for building proofs of such type in future.

Thanks in advance. Plz write.

Perhaps it would help if you sketched the proof you are familiar with. — lulu, Feb 07 '20 at 18:51
The sequence $\sin n$ has infinite many limit numbers, so there is no limit actually... — dmtri, Feb 09 '20 at 08:07

score 1 · Answer 1 · edited Feb 09 '20 at 12:11

1

Prove that $ \sin n$, $\sin (n+1)$ and $\sin (n+2)$ are not all close together.

edited Feb 09 '20 at 12:11

dmtri

3,270

answered Feb 07 '20 at 18:58

gnasher729

10,113

3

This is a little terse, and looks at first glance to be a non-answer & hence deletable. Can you flesh your argument out a little, please? – kimchi lover Feb 07 '20 at 19:24

The sequence S:=(sin n) is divergent.

1 Answers1