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Is there a way to find a closed form solution for: (Note that base is $2$)

$\displaystyle\sum_{i=1}^n\log_2(i)$

thanks for any help Can't find a formula for this

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    @ChrisTaylor: It makes the question title ambiguous and confusing. Is the question about the power series for the logarithm of $i=\sqrt{-1}$? (which is what I thought when I first saw the question title)2012-02-01

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$ \sum_{i=1}^n \log i = \log \left(\prod_{i=1}^n i\right) = \log (n!).$

But note that the left hand site is actually easier to compute (numerically).

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    Note that you can obtain nice asymptotics for the whole expression by Stirling's formula.2012-02-01