Show whether a funtion converges

1. Mar 8, 2006

Gott_ist_tot

I have a homework problem to show whether a funtion converges.

the sum from k =1 to infinity of 1/(k+6)
The answer says that it diverges although I do not understand this. Doesn't the limit approach zero? It makes sense due to the p-test where p = 1. But t should approach zero. thanks for any help.

2. Mar 8, 2006

Hurkyl

Staff Emeritus
The question is asking if

$$\sum_{k=1}^{+\infty} \frac{1}{k+6}$$

converges, not if

$$\lim_{k \rightarrow +\infty} \frac{1}{k+6}$$

converges.

3. Mar 8, 2006

Captain Zappo

Try some of the convergence tests that you know.

You can try the ratio test, direct comparison, the limit comparison test, etc...

Give us some attempts and we'll see if we can help you out.

4. Mar 8, 2006

Gott_ist_tot

Yeah, I got the answer with the p test. I will look over the proof really well. I just don't grasp how you can effectively be adding zero to the sum and it does not converge to zero also. I just know that it does.

5. Mar 8, 2006

Hurkyl

Staff Emeritus
You could be actually adding 0 to the sum, and still not have it converge to zero. e.g. 1 + 0 + 0 + 0 + 0 + ... = 1

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