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Good day! Is there a formula that approximate the summation of natural logarithm of N as N runs from 1 to infinity?

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  • $\begingroup$ Do you mean $\log1+\dots+\log N$? Running the sum to infinity wouldn't work. $\endgroup$
    – user147263
    May 22, 2015 at 0:24

2 Answers 2

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The sum from 1 to n is the log of n!. Look up Stirling's formula.

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If you mean $\log(1)+\cdots+\log(N)$, then

\begin{align} \sum_{i=1}^N\log(i)=\log(\Gamma(N+1)) \end{align}

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