SUmmation of natural logarithm

Question

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

Do you mean $\log1+\dots+\log N$? Running the sum to infinity wouldn't work. — , May 22 '15 at 00:24

score 0 · Answer 1 · answered May 22 '15 at 00:26

0

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

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

answered May 22 '15 at 00:26

user85503

score 0 · Accepted Answer · answered May 22 '15 at 00:48

0

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

answered May 22 '15 at 00:48

marty cohen

2 Answers2