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Thread: Help with sequence formula

  1. March 6th 2013, 10:35 AM #1
    amyw
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    Help with sequence formula

    I have the sequence: <1, 3/2, 7/4, 15/8, 31/16, 63/32,...> and I need to find a formula to describe it. Can anyone help? I must have missed the day when this was taught.
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  2. March 6th 2013, 07:21 PM #2
    TheEmptySet
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    Re: Help with sequence formula

    Quote Originally Posted by amyw View Post
    I have the sequence: <1, 3/2, 7/4, 15/8, 31/16, 63/32,...> and I need to find a formula to describe it. Can anyone help? I must have missed the day when this was taught.
    The numerator can be defined recursively. Let

    Here is a hint: the number is the sum of the geometric series 2^n

    2^{0}=1 \\ 2^{0}+2^1=3 \\ 2^{0}+2^1+2^2=7 \\ 2^{0}+2^1+2^2+2^3=15

    So what does

    \sum_{k=0}^{n}2^k=?
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