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Homework Help: Convergence question

  1. Mar 30, 2010 #1
    Q: Is the series 1/2n convergent or divergent? If convergent find it's sum.

    I see that the limit as n goes to infinity is zero but that does not prove C or D. It seems like it would be divergent but why? How can that be shown?

    Any direction/help would be greatly appreciated.
     
  2. jcsd
  3. Mar 30, 2010 #2

    Dick

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    Try an integral test. Do you know that one?
     
  4. Mar 30, 2010 #3
    Yes I do but I shouldn't lol (we haven't gotten to that in class). We have covered the harmonic series and shown it is D.

    I also notice I can't do a comparison to 1/n since 1/n > 1/2n.
    Would the argument 1/2 * 1/n = 1/2 x divergent = D make sense?
     
  5. Mar 30, 2010 #4

    Dick

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    Sure. If a series is divergent, then any nonzero constant times the series is also divergent. That's true. But do you have a theorem or something to justify it rather than just writing divergent*(1/2)=divergent? That just seems a little sloppy.
     
  6. Mar 30, 2010 #5
    Yeah I know. I'm typing on this forum from my phone so it's tough to be elegant lol. The question only asks C or D but I kinda wanted to know for my own purposes but thanks for the help in understanding it. :)
     
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