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Converge or not

  1. Jun 5, 2009 #1
    Does the series [tex]\sum\frac{2}{2^{n}}[/tex]


    converge??

    (Note that bounds on the running index n are from 1 to infinity)

    I have tried ratio test but it returned a value of 1 (showing nothing).

    I can see from the table function on my calulator that the term eventually diminsh to (not including zero).

    Any help would be appreciated.
     
  2. jcsd
  3. Jun 5, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Can you show how you did the ratio test? The ratio is NOT 1.
     
  4. Jun 5, 2009 #3
    Rememer, you can pull anything not involving an "n" out of the summation. So the 2 in the numerator can come out. Then you have

    2 (SUM) 1/2^n

    This can also be written as

    2 (SUM) (1/2)^n

    You should be able to recognize the SUM as a notable one, and use the rules pertaining to that kind of summation to determine whether or not it converges. And if it converges, does multiplying by 2 change any of that?
     
  5. Jun 5, 2009 #4
    Sorry fellas the question should read

    Does the series [tex]\sum\frac{n}{2^{n}}[/tex]


    converge??

    (Note that bounds on the running index n are from 1 to infinity)

    I have tried ratio test but it returned a value of 1 (showing nothing).

    I can see from the table function on my calulator that the term eventually diminsh to (not including) zero.

    Any help would be appreciated
     
  6. Jun 5, 2009 #5

    Dick

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    Homework Helper

    Ratio test should still not give you a value of 1. Can you show how you got that?
     
  7. Jun 5, 2009 #6

    nicksauce

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    What comes to my mind would be doing a comparison test with the integral of x*exp(-x).
     
  8. Jun 6, 2009 #7

    Mark44

    Staff: Mentor

    What Dick said. The ratio test is definitely the test to use. If you got a limit of 1, you're doing something wrong.
     
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