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Several Series Test Questions

  1. Sep 12, 2006 #1

    G01

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    Hey everyone, I have some problems here involving the comparision test and Alternating series tests for series. I've solved most but there are about five i'm lost on. All I'm asking for is a couple hints. Thanks Theres only one alternating series question so I'll put that first.

    AST:
    [tex]\sum^{\infty}_{n=1} (-1)^nsin(\pi/n) [/tex]

    Comparison or Limit Comparison:

    [tex]\sum^{\infty}_{n=2} \frac{n^2+1}{n^3-1}[/tex]

    [tex]\sum^{\infty}_{n=1} \frac{1}{n!} [/tex]

    [tex] \sum^{infty}_{n=1} \sin(\frac{1}{n}) [/tex]

    OK and this last one :

    [tex]\sum^{\infty}_{n=1} \frac{5+2n}{(1+n^2)^2}[/tex]



    I know I dont have any work but I'm stuck on these five. All I'm asking for is a couple hints thanks in advance.
     
    Last edited: Sep 12, 2006
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  3. Sep 12, 2006 #2

    StatusX

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    You can do a little work. Do you understand these methods? Where exactly are you getting stuck?
     
  4. Sep 12, 2006 #3

    G01

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    Alright for the comparison or limit test problems I get stuck trying to find the series to compare it too. Is there any advice that makes picking a comarison series easier? I'l work on these a little more and post what I get.
     
  5. Sep 12, 2006 #4

    G01

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    Yeah I got the answer for the first comparison test question, that is divergent I ended up comparing it to N^2/N^3.
     
  6. Sep 12, 2006 #5

    StatusX

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    OK, that works. The same idea for works for the last one. For the sin(1/n) one, consider what sin(x) looks like as x->0. For the n! one, think geometric series.
     
  7. Sep 12, 2006 #6

    G01

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    OK, got the last one. I multiplied out the denominator and then found a comparison. Still stuck on the sin and factorial ones tough.
     
    Last edited: Sep 12, 2006
  8. Sep 12, 2006 #7

    StatusX

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    So.... do you know what sin(x) looks like as x->0 or what a geometric series is?
     
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