1

I'm trying to determine at what x values an infinite series of the function $-sin(nx)$ converges. I think I may be over thinking this relatively simple question. But I just want to verify that I'm on the right path. Because $-sin(nx)$ is always between -1, and 1, couldn't we just say that this function is convergent for all values of x (positive or negative) because a comparison test with a sequence is not needed?

kris
  • 187
  • Do you mean to ask about the MacLaurin series for the function? – David Nov 28 '14 at 13:04
  • there seem to be many related problems on MSE didn't try to find them all, here is one http://math.stackexchange.com/questions/36732/is-the-sum-of-sinn-n-convergent-or-divergent – Mirko Nov 28 '14 at 13:04

1 Answers1

0

You can't say that function $-\sin(nx)$ converges for any x because it doesn't. This function takes all values between -1 and 1 for period $\frac{2\pi}{n}$ where n belongs to natural numbers and same for all n and all x.

Lale221
  • 111