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Determine if the sum Converges or Diverges

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data

    dve9e.jpg

    3. The attempt at a solution

    1. I have no idea. I know that the summation of the series converges.


    2. I think it would diverge because the limit of the function does not equal zero.


    3. I have tried the ratio test and got 1. Can't use the alternating series test because when ignoring signs the function increases.
     
  2. jcsd
  3. Dec 4, 2011 #2

    Dick

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    For 3 what's the limit of (5n-1)/(n+5) and what does that tell you about convergence? For 1 I think they might be asking you to estimate the difference using an integral.
     
  4. Dec 4, 2011 #3

    hunt_mat

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    2) is correct
    3) Think about the function [itex]f(x)=\ln x[/itex]
     
    Last edited: Dec 4, 2011
  5. Dec 4, 2011 #4
    The limit of (5n-1)/(n+5) as x approaches infinity equals 5 thus meaning that the series in divergent? I think
     
  6. Dec 4, 2011 #5
    [/QUOTE]

    I'm not sure what [itex]f(x)=\ln x[/quote] means. Can you plus explain.
     
  7. Dec 4, 2011 #6

    Dick

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    Right. If the nth term of a series doesn't approach 0 then it's always divergent. Now can you write an integral that's greater than the difference in 1?
     
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