# Homework Help: Trouble to find the test

1. Nov 27, 2013

### Jbreezy

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

Test the series for convergence or divergence

2. Relevant equations

A_n = Ʃ 1/(2+sin(k)) from k = 1 to ∞

3. The attempt at a solution

I looked at this and I thought that sin(k) does not have a limit as k goes to infinity. So I was thinking that Lim k--> ∞ A_n = Does not exist. So, the series is divergent. I origonally thought to use the alternating series test since A_n is alternating but I didn't really get anywhere. How is my reasoning with this problem? Right track or no? Thanks,
J

2. Nov 27, 2013

### LCKurtz

That is not an alternating series. Every term is positive. In the denominator you have $1\le 2+\sin(k)\le 3$. Although your limit argument is OK, you can also use this inequality to understimate your series with an obviously divergent one.

3. Nov 27, 2013

### Jbreezy

Why isn't it alternating? I was thinking it was since sin(k) is cyclic. You know between -1 and 1.

$1\le 2+\sin(k)\le 3$ You mean I want something smaller that diverges?

4. Nov 27, 2013

### Office_Shredder

Staff Emeritus
Jbreezy, what is the definition of an alternating series?

5. Nov 27, 2013

### Jbreezy

Alternates. A_n+1 < A_n and Limit n--> infinity is 0.

6. Nov 27, 2013

### LCKurtz

Every term in the series is positive.

It is true that $\sin k$ is between $-1$ and $1$. But there is nothing "cyclic" about it, whatever you mean by cyclic.

Yes, a smaller series which is divergent.

7. Nov 27, 2013

### LCKurtz

JBreezy, if, after as long as you have been posting, you can't bring yourself to quote the message to which you are replying, our conversation is going to be very short.

8. Nov 27, 2013

### Office_Shredder

Staff Emeritus
No, an alternating series is one in which the sign of the terms changes every time n increases by 1. What you stated are the conditions required for the alternating series convergence test to be used, the conditions that are needed on top of the series being alternating.

So we go back to the question of: is this series alternating? Do the terms change sign every time? The answer to that is no: 1/(2+sin(k)) does not change signs every time k increases by 1.

9. Nov 27, 2013

### Jbreezy

Yeah. Followed.

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