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Math Help - What is the sum of ln(i) from 1 to n in terms of n.

  1. #1
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    What is the sum of ln(i) from 1 to n in terms of n.

    f(n) = \sum_{i = 1}^{n} log_2(i)
    Having a hard time figuring this one out.
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  2. #2
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    My guess is.

     \log_2(1)+\log_2(2)+\log_2(3)+\dots+\log_2(n-1)+\log_2(n)

     \log_2(1\times 2\times3\times\dots\times (n-1)\times n)

     \log_2(n!)
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  3. #3
    MHF Contributor chisigma's Avatar
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    Applying the basic properties of the logarithms You obtain...

    \sum_{i=1}^{n}\log_{2} i = \log_{2} \prod_{i=1}^{n} i = \log_{2} n!

    Kind regards

    \chi \sigma
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