Question

Determine whether the sequence converges or diverges. an =(-1)^n [(n+2)/(3n-1)]

Answer 1

Have you learned alternating series test?

Answer 2

not really.

Answer 3

but yeah

Answer 4

o.k. Its been a while, let me dust off the old brain....

Answer 5

lol, it's alright, take all the time you need ^_^

Answer 6

It looks like you have to do the alternating series test. I'm looking over my old notes....but you said you have not lean this yet?

Answer 7

I'm not sure if I did, does it have to do with finding the absolute value of an? as an approaches infinity?

Answer 8

not the absolute value. The (-1)^n gives a hint that its alternating series.

Answer 9

yes I know it is and it alternates between -1 and 1

Answer 10

Usually when you see that then you know that its alternating series.

Answer 11

o.k

Answer 12

yep :)

Answer 13

well I am really rusty on my cal 2. You can google paul's online math notes to get better clarification. I used his notes to get through cal 1 -cal 3.

Answer 14

I've done that before, but thanks anyways :)

Answer 15

I'll figure something out ^_^

Answer 16

oh, o.k. Sorry for not being able to help you.

Answer 17

no, thank you for your time dear, atleast you've tried :)

Answer 18

I very much appreciate it ^_^

Answer 19

yeah. Ill keep looking at it. I hate it when I use to know something and cannot figure it out.

Answer 20

lol, it's alright, I'll visit my prof tomorrow before the midterm, he has submitted a special office our just in case :) it's alright.

Answer 21

Have you done the test for divergence?

Answer 22

you mean discussing the convergence/divergence of a sequence ,yes

Answer 23

Well i was looking up videos from patrickjmt.com and he gives examples about alternating series and he points out how its a two step process in figuring out whether it diverges or converges. He recommends first taking the limit of an and see whether it does not exists or it does not equal zero, if you find that its either of these then in is divergent.

Answer 24

I did find the limit

Answer 25

I first multiplied (-1)^n to the fraction, then simplified + found the limit.

Answer 26

The way I remember doing it is that you do not look at the (-1)^n . Just (n+2)/(3n-1). This will now be your bn. Take this limit. It it does not exist or does not equal to zero then it is considered divergent.

Answer 27

If it does equal to zero, then you have to check whether bn+1 is less than bn. If you pove this also, then you know that it is convergent.

Answer 28

you mean I have to divide the question into 2 parts? like this:\[ \lim_{n \rightarrow \infty}(-1)^n . \lim_{n \rightarrow \infty}(n+2)/(n+3)\]
?

Answer 29

No, just the second limit.

Answer 30

find that limt.

Answer 31

why? what about the first limit?

Answer 32

The (-1)^n tells us that its alternating series, so we have to show whether our bn which is what we define as (n+2)/(n+3) has a limit which equals to 0. It it does that we also have to prove that bn+1 is less than bn. By satisfying these two conditions than we can say that its convergent. If while we take the limit as n goes to infinity of bn, we see that the limit does not exist or that it does not equal to zero than we can say that it is divergent.

Answer 33

That is how I would approach this problem. Just check w/ your professor like you said you were going to do. I am not an expert at this, just recovering info from what i learned.

Answer 34

Well good luck on your midterm. Sorry if I caused any confusion.

Answer 35

thank you, I think I got what you've meant, all I have to do is review what you've said again, thanks dear ^_^