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Math Help - proof of sum

  1. #1
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    proof of sum

    I'm sorry that the thread title isn't descriptive at all, but I didn't know what to name it.

    I have to take this sum:
    sum from 0 to log base 2 of (n-1) of (n((3/2)^k)) - Wolfram|Alpha

    and prove that for every positive integer n that is a power of 2, the sum is:
    2(n^(log3/log2) - n)

    can anyone help? thanks in advance
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  2. #2
    Grand Panjandrum
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    Re: proof of sum

    Quote Originally Posted by giygaskeptpraying View Post
    I'm sorry that the thread title isn't descriptive at all, but I didn't know what to name it.

    I have to take this sum:
    sum from 0 to log base 2 of (n-1) of (n((3/2)^k)) - Wolfram|Alpha

    and prove that for every positive integer n that is a power of 2, the sum is:
    2(n^(log3/log2) - n)

    can anyone help? thanks in advance
    Your sum is:

     \sum_{k=0}^{\frac{\log(-1+n)}{\log(2)}} n.\left( \frac{3}{2}\right)^k

    1. Suppose n=2^r

    2. The sum is not well defined as the upper limit of summation is not an integer, so I suppose it means:

    \left\lfloor \frac{\log(n-1)}{\log(2)}\right\rfloor=\lfloor \log_2(n-1)\rfloor = r-1

    3. The series is a finite geometric series.

    CB
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