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Comparison test for series

  1. Jun 3, 2014 #1
    I'm trying to find if this series converges or diverges using the comparison test:
    attachment.php?attachmentid=70324&stc=1&d=1401850854.png

    and the answer goes:
    attachment.php?attachmentid=70325&stc=1&d=1401850854.png


    My problem is, Im not sure how to go from 1/2^(n+1) to 1/2(1/2)^n.

    can you please explain that to me
     

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  2. jcsd
  3. Jun 3, 2014 #2

    Matterwave

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    $$\frac{1}{2^{n+1}}=\frac{1}{2\cdot 2^n}=\frac{1}{2}\frac{1}{2^n}=\frac{1}{2}\left(\frac{1}{2}\right)^n$$
     
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