1. Nov 1, 2009

clickyclicky

I have a test on this stuff and I'm confused about some things.

First, how do I show work to this problem?

I know that its absolute value diverge but I don't know how to show the work. Also not sure how to show the work for alternating series test. Not sure how to show that the it's decreasing.

I also have a question about sequences.

I should take the limit, but the sin throws me off.

Thanks,

clickyclicky

Last edited: Nov 1, 2009
2. Nov 1, 2009

Staff: Mentor

Then how do you know this? If it's because the answer in the back of the book says so, then you are not very far along in working this problem.
What are the conditions that have to be satisfied so you can use the alternating series test?
Let an = ln(n)/sqrt(n). Can you think of some calculus technique that would show whether this function of n is increasing or decreasing?

3. Nov 1, 2009

rochfor1

For the sequence, try multiplying the numerator and denominator by 1/n and then taking the limit. (Remember the Squeeze theorem.)

4. Nov 1, 2009

clickyclicky

For the first one I know that 1/√n diverges. If there's a ln n on the top it'll make the series slower.

If I try the alternating series test, I get 0 when I take the limit, but I can't figure out how to show that the function is decreasing. I tried to take the derivative but it doesn't tell me anything.

I'm not sure how to apply the squeeze theorem to the second one.

5. Nov 1, 2009

rochfor1

You don't evaluate the whole limit using the Squeeze theorem, just use it to show that sin n/n and sin^2 n/n go to 0.

6. Nov 1, 2009

clickyclicky

Are you saying that I should show that sin n is bounded and therefore goes to 0?

7. Nov 1, 2009

rochfor1

I'm saying exactly what I mean. I leave the details of the squeeze theorem to you.

8. Nov 1, 2009

clickyclicky

A quick look in the textbook and I see what you mean. Thanks.