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Homework Help: General question about convergence of series

  1. May 14, 2005 #1
    In general, is it true that if a sequence has a limit that it converges and if it does not have a limit that it diverges?when i say have a limit i mean that the limit exists.
     
  2. jcsd
  3. May 14, 2005 #2
    Given [tex]\sum_{n=0}^{\infty} a_n[/tex]

    if the series converges, then

    [tex]\lim_{n\rightarrow\infty}a_n = 0[/tex]

    This does not mean that if the limit = 0 it converges, but that it has a possibility to converge. If the limit does not equal 0, the series diverges.
     
  4. May 14, 2005 #3

    James R

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    Are you talking about sequences or series, RadiationX?

    By definition, if a sequence has a finite limit, then it converges to that limit.
     
  5. May 14, 2005 #4
    yes i was talking about sequences
     
  6. May 15, 2005 #5

    HallsofIvy

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    Yes. "Converge" is DEFINED as "has a limit". "Diverge" is defined as "does not have a limit".
     
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