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Convergent/Divergent Sequences

  1. Sep 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Determine whether the sequence is convergent or divergent. Find limits for convergent sequences.

    [tex]c_{1} = 4,[/tex]

    [tex]c_{n+1} = -\frac{c_{n}}{n^{2}}[/tex] for [tex]n \geq 1[/tex]


    2. Relevant equations
    [tex]lim_{n\rightarrow\infty} a_{n} = L[/tex]

    Where L is a number.

    3. The attempt at a solution

    Okay so when n=1,

    [tex]c_{2} = -4[/tex]

    n=2,

    [tex]c_{3} = 1[/tex]

    n=3,

    [tex]c_{4} = -\frac{1}{9}[/tex]

    I don't seem to be approaching a certain value here and I'm not sure how I can take the limit as n goes to infinity of the general term, because the general term itself depends on the previous term.

    Any ideas?
     
  2. jcsd
  3. Sep 15, 2010 #2

    jgens

    User Avatar
    Gold Member

    Why don't you try looking at a few more cases before deciding that it doesn't appear to be approaching a particular value.
     
  4. Sep 15, 2010 #3
    Okay.

    n=4,

    [tex]c_{5} = \frac{1}{144} [/tex]

    n=5,

    [tex]c_{5} = \frac{-1}{3600} [/tex]

    Whoops! The fact that it was flipping signs confused me, this things going to zero, whether it has a negative or not!
     
  5. Sep 15, 2010 #4
    Yes, it goes to zero.
     
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