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Infinite Series

  1. Jul 9, 2008 #1
    1. The problem statement, all variables and given/known data

    Is the series from n=1 to infinity of 3/n converging or diverging?

    2. Relevant equations


    3. The attempt at a solution

    Since 3/n is not a geometric series, my guess is that we can just use the Test for Divergence and take it's limit to see if it's converging or diverging. As n->infinity, 3/n -> 0 and lim = 0, so it's converging.

    However, I am not sure if this is right way to go about it.
     
  2. jcsd
  3. Jul 9, 2008 #2

    Tom Mattson

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    Correct.

    Not a bad guess, but beware that the Test for Divergence cannot tell you if a series converges (hence, its name).

    Wrong. The Test for Divergence says that:

    [tex]\lim_{n\rightarrow\infty}a_n \neq 0 \Rightarrow \sum_{n=1}^\infty a_n[/tex] diverges.

    Equivalently, it says that:

    [tex]\sum_{n=1}^\infty a_n[/tex] converges [tex]\Rightarrow \lim_{n\rightarrow\infty}a_n = 0[/tex]

    If the limit is zero, then the test yields no information and you have to use another test.
     
  4. Jul 9, 2008 #3
    So I would have to treat it as a Harmonic Series?
     
  5. Jul 9, 2008 #4

    Tom Mattson

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    It is a harmonic series.
     
  6. Jul 9, 2008 #5
    Alright, thank you for your help.
     
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