# Series convergence

1. Nov 14, 2012

### Bipolarity

1. The problem statement, all variables and given/known data

Determine whether the following series diverges, converges conditionally, or converges absolutely.

$$\sum^{\infty}_{n=1}sin(\frac{1}{n^{4}})$$

2. Relevant equations

3. The attempt at a solution
This was on today's test, and was the only problem I wasn't able to solve. I doubt my teacher will be going over these, and in any case his explanations never satisfy me, so could someone help me with this?

According to the nth term test, the limit of the sequence is 0, since sin(x) is continuous, so the function doesn't necessarily diverge.

Integral test cant be applied because the sequence is not monotonic. Root test serves no purpose. Limit comparison might work, but with what? Ratio does not work (I think?).

How might I approach this?

BiP

2. Nov 14, 2012

### Zondrina

Hedi beat me to it down below VVV haha. I forgot that something bigger that diverges tells you nothing.

Last edited: Nov 14, 2012
3. Nov 14, 2012

### hedipaldi

use limit comparison with 1/n^4.for large n this is a positive series.

4. Nov 14, 2012

### Bipolarity

Thanks!!!

But damn!! I wish I thought of that in the test! Oh well.

BiP