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Geometric Series Test Rather Than Integral Test

  1. Oct 6, 2012 #1
    1. The problem statement, all variables and given/known data
    [itex]\sum_{n=1}^{\infty} \frac{1}{2^n}[/itex]


    2. Relevant equations



    3. The attempt at a solution
    Could I some how manipulate this to fit a geometric series, so that I may instead use the geometric series test?
     
  2. jcsd
  3. Oct 6, 2012 #2

    HallsofIvy

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    [tex]\frac{1}{2^n}= \left(\frac{1}{2}\right)^n[/tex]
     
  4. Oct 6, 2012 #3

    SammyS

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    Hint:

    No manipulation is required.
     
  5. Oct 6, 2012 #4
    Well, I was told by my teacher that n couldn't equal one for the geometric series to be implemented, was he, perhaps, wrong?
     
  6. Oct 6, 2012 #5

    SammyS

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    Do you mean, n can't start at 1, it must start at zero?

    If so factor 1/2 out of your series & change the index accordingly,

    else,

    Add 1 to your series so that it starts at n=0, and subtract 1 from your result.
     
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