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Homework Help: Converges or diverges?

  1. Jan 13, 2010 #1
    Ok, so the problem is [(3^-n)+(n^-1)] and I have to determine if it converges are diverges. from n=1 to inf. The problem is that individually I know that the 3^-n should converge and that n^-1 should diverge. But I don't understand what happens when your taking the series of the two combines. I think it would diverge, because of the n^-1, but I don;t know what test to prove it or if I even have the right idea. If anyone has any suggestions of a test to do, I tried the root test but found it to be 1 which is inconclusive, and I dont know where to go with this problem.
  2. jcsd
  3. Jan 13, 2010 #2
    You know that 1/n diverges from the integral test, and that 3-n is only making the sum bigger, so it diverges.
  4. Jan 13, 2010 #3
    Thank you so much. I just wasn't sure if you could do that.
  5. Jan 13, 2010 #4


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    Homework Helper

    To firm this up, if [tex] a_n = e^{-n} + n^{-1} [/tex] and [tex] b_n = n^{-1} [/tex].
    you can use the comparison test to show that [tex] \sum_{n=1}^\infty a_n [/tex] diverges.
  6. Jan 14, 2010 #5


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    Science Advisor

    By the way, it would have been clearer if you had stated from the start that the question was whether or not the series [itex]e^{-n}+n^{-1}[/itex] converges. Of course, the sequence obviously converges to 0 so everyone assumed you mean "series" but it was ambiguous which you meant.
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