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Homework Help: Serie Converge/Diverge

  1. Feb 21, 2008 #1
    Firs Question

    If the serie


    ∑ Xn = (1/n²)
    n=1

    converge, then the serie |Xn| converge?

    Second question

    the serie

    ∑ X^n / [fat(n)] diverge?
    n=1

    where fat(n) = n(n-1)(n-2)...4.3.2.1

    Its important know the value of X in X^n?
     
  2. jcsd
  3. Feb 21, 2008 #2

    NateTG

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  4. Feb 21, 2008 #3
    1)what is the || of 1/n^2?? think
    2) search for geometric series and the hierarchy of infinities..

    regards
    marco
     
  5. Feb 21, 2008 #4

    HallsofIvy

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    [tex]\sum_{n=0}^1 \frac{x^n}{n!}[/tex]
    is a well known Taylor's series for a simple function and your sum is only slightly different.
     
  6. Feb 21, 2008 #5
    my answer
    1)

    ∑ Xn = (1/n²) = 1 + 1/4 + 1/9 ... its a p-serie and converge because p=2>1.
    n=1
    and

    ∑ |Xn| = (1/n²) = 1 + 1/4 + ... its the same.. so its converge too.
    n=1

    2) converge using comparison test, no dought!
     
  7. Feb 21, 2008 #6

    Dick

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    Better to use a ratio test. It will make it easy to see why the value of x doesn't matter.
     
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