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Infinite series please help.

  1. Jun 23, 2005 #1
    I'm having a little trouble with the following problem. here it is...

    Determinte whether a_n is convergent for...

    [tex] a_n = \frac{2n}{3n+1}[/tex]

    How would i go about solving this? Can i just simply take the limit and use L'Hospital's rule to see if it diverges or converges? Or is it a little more complicated than that? Im asking this because in this section we're studying geometric series, and that doesnt look like a geo series to me since n is not in the exponent. Any help would be appreciated, thanks.
     
  2. jcsd
  3. Jun 23, 2005 #2
    hello there

    that aint a series, its a sequence

    well to find if a_n is convergent, you would want to see what happens as n goes to infinity, and to do that divide the numerator and the denominator by the highest power in a_n, and im sure you should know what happens to 1/n as n goes to infinty

    steven
     
  4. Jun 23, 2005 #3
    one more thing

    if it is a series i would use either the
    comparision test
    or the
    limit comparision test

    steven
     
  5. Jun 24, 2005 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Series or sequence?

    You don't need anything as complicated as L'Hospital's rule to determine this. If you mean the sequence [tex]\frac{2n}{3n+1}[/tex], just divide both numerator and denominator by n to get [tex]\frac{2}{3+\frac{1}{n}}[/tex]. What happens to that as n goes to infinity?

    If you mean the series [tex]\Sigma_{n=1}^{\infty}\frac{3n}{3n+1}[/tex], that's also easy after you know the limit of the sequence- in order that the series [tex]\Sigma a_n[/tex] converge, the sequence {an} must converge to 0.
     
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