Comparison test for series

  • Thread starter uzman1243
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  • #1
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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
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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