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Math Help - Finding Interval of Convergence

  1. #1
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    Finding Interval of Convergence

    Can anyone help me solve this?

    My answer is 5.
    My friend's got 17.

    Im confused.
    Attached Thumbnails Attached Thumbnails Finding Interval of Convergence-interval-convergence.png  
    Last edited by weijing85; April 19th 2013 at 07:15 PM. Reason: missing attachment
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  2. #2
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    Re: Finding Interval of Convergence

    Quote Originally Posted by weijing85 View Post
    Can anyone help me solve this?

    My answer is 5.
    My friend's got 17.

    Im confused.

    The series

    \frac{1}{1+z}=1-z+z^2-z^3+z^5-z^5+...

    is convergent if and only if |z|<1.

    In your case, z=\frac{x-12}{5}, so |x-12|<5. If x\geq 12, then you get x-12<5 \implies x<17. If x\leq 12, you get -x+12<5 \implies x> 7. Thus your interval of convergence is (7,17)

    So your friend is correct.
    Last edited by Gusbob; April 20th 2013 at 02:27 AM.
    Thanks from weijing85
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  3. #3
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    Re: Finding Interval of Convergence

    thanks! ((:
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