1. ## alternating series #2

$\displaystyle \sum^{\infty}_{n=1} (-1) sin(\frac{6\pi}{n})$

Would I compare this to $\displaystyle sin\frac{1}{n}$?

2. Is this alternating or can we pull out the negative one?

Do a limit comp to the harmonic series, which diverges. Then use let $\displaystyle m=1/n$ and use

$\displaystyle {\sin m\over m}$ goes to one as $\displaystyle m\to 0$.

3. Originally Posted by matheagle
is this alternating or can we pull out the negative one?
Are you asking me? This is in the alternating series section of my homework. I think that I can pull it out.

4. Originally Posted by mollymcf2009
Are you asking me? This is in the alternating series section of my homework. I think that I can pull it out.
yes, do you mean $\displaystyle (-1)$ or $\displaystyle (-1)^n$

5. Originally Posted by matheagle
Is this alternating or can we pull out the negative one?

Do a limit comp to the harmonic series, which diverges. Then use let $\displaystyle m=1/n$ and use

$\displaystyle {\sin m\over m}$ goes to one as $\displaystyle m\to 0$.
But I don't understand why you did that? Why does sin(m)/m go to 1 as m goes to 0?

6. Originally Posted by matheagle
yes, do you mean $\displaystyle (-1)$ or $\displaystyle (-1)^n$
It is $\displaystyle (-1)^n$ so since there is an n as an exponent I CAN'T pull it out? I am CONFUSED!!!!!

7. Originally Posted by mollymcf2009
But I don't understand why you did that? Why does sin(m)/m go to 1 as m goes to 0?
basic calculus one, or use l'hopital's rule