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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    Have you learned alternating series test?

  2. anonymous
    • 5 years ago
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    not really.

  3. anonymous
    • 5 years ago
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    but yeah

  4. anonymous
    • 5 years ago
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    o.k. Its been a while, let me dust off the old brain....

  5. anonymous
    • 5 years ago
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    lol, it's alright, take all the time you need ^_^

  6. anonymous
    • 5 years ago
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    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?

  7. anonymous
    • 5 years ago
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    I'm not sure if I did, does it have to do with finding the absolute value of an? as an approaches infinity?

  8. anonymous
    • 5 years ago
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    not the absolute value. The (-1)^n gives a hint that its alternating series.

  9. anonymous
    • 5 years ago
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    yes I know it is and it alternates between -1 and 1

  10. anonymous
    • 5 years ago
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    Usually when you see that then you know that its alternating series.

  11. anonymous
    • 5 years ago
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    o.k

  12. anonymous
    • 5 years ago
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    yep :)

  13. anonymous
    • 5 years ago
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    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.

  14. anonymous
    • 5 years ago
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    I've done that before, but thanks anyways :)

  15. anonymous
    • 5 years ago
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    I'll figure something out ^_^

  16. anonymous
    • 5 years ago
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    oh, o.k. Sorry for not being able to help you.

  17. anonymous
    • 5 years ago
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    no, thank you for your time dear, atleast you've tried :)

  18. anonymous
    • 5 years ago
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    I very much appreciate it ^_^

  19. anonymous
    • 5 years ago
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    yeah. Ill keep looking at it. I hate it when I use to know something and cannot figure it out.

  20. anonymous
    • 5 years ago
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    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.

  21. anonymous
    • 5 years ago
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    Have you done the test for divergence?

  22. anonymous
    • 5 years ago
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    you mean discussing the convergence/divergence of a sequence ,yes

  23. anonymous
    • 5 years ago
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    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.

  24. anonymous
    • 5 years ago
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    I did find the limit

  25. anonymous
    • 5 years ago
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    I first multiplied (-1)^n to the fraction, then simplified + found the limit.

  26. anonymous
    • 5 years ago
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    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.

  27. anonymous
    • 5 years ago
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    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.

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

  29. anonymous
    • 5 years ago
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    No, just the second limit.

  30. anonymous
    • 5 years ago
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    find that limt.

  31. anonymous
    • 5 years ago
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    why? what about the first limit?

  32. anonymous
    • 5 years ago
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    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.

  33. anonymous
    • 5 years ago
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    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.

  34. anonymous
    • 5 years ago
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    Well good luck on your midterm. Sorry if I caused any confusion.

  35. anonymous
    • 5 years ago
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    thank you, I think I got what you've meant, all I have to do is review what you've said again, thanks dear ^_^

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