alternating series #2

**mollymcf2009** · March 29th 2009, 01:40 PM

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

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

**matheagle** · March 29th 2009, 02:02 PM

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

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

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

**mollymcf2009** · March 29th 2009, 02:05 PM

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.

**matheagle** · March 29th 2009, 02:07 PM

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 $(-1)$ or $(-1)^n$

**mollymcf2009** · March 29th 2009, 02:09 PM

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 $m=1/n$ and use

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

But I don't understand why you did that? Why does sin(m)/m go to 1 as m goes to 0?

**mollymcf2009** · March 29th 2009, 02:11 PM

Originally Posted by matheagle

yes, do you mean $(-1)$ or $(-1)^n$

It is $(-1)^n$ so since there is an n as an exponent I CAN'T pull it out? I am CONFUSED!!!!!

**matheagle** · March 29th 2009, 03:20 PM

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

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