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3 true or false

  1. Apr 23, 2006 #1
    True or false, justify your answer

    1) If [tex]\sum_{n=1}^\infty a_n[/tex] converges, then [tex]\sum_{n=1}^\infty (-1)^n \ a_n[/tex] converges.

    2) If [tex]\sum_{n=1}^\infty a_n[/tex] converges and [tex]\sum_{n=1}^\infty (-1)^n \ a_n[/tex] converges, then [tex]\sum_{n=1}^\infty a_n[/tex] converges absolutely.

    3) If [tex]\sum_{n=1}^\infty a_n[/tex] converges absolutely, then [tex]\sum_{n=1}^\infty (-1)^n \ a_n[/tex] converges absolutely.

    Can anybody help me with this one?

    Thanks in advance
     
    Last edited: Apr 23, 2006
  2. jcsd
  3. Apr 23, 2006 #2

    Hootenanny

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    your [t e x] tags must be in lower case.

    ~H
     
  4. Apr 23, 2006 #3
    Thank you, Hootenanny. That fixed everything!
     
  5. Apr 23, 2006 #4

    Hootenanny

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    RE: Your question, what are the criteria for absolute convergence?

    ~H
     
  6. Apr 23, 2006 #5

    HallsofIvy

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    Or, what is the definition of "absolute convergence"?
     
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