number theory - Summation of logs

Are there any useful identities for quickly calculating the sum of consecutive logs? For example $\sum_{k=1}^{N} log(k)$ or something to this effect. I should add that I am writing code to do this (as opposed to doing this on a calculator) so N can be very large.

Answer

For large $N$, we have $N!\approx N^Ne^{-N}\sqrt {2\pi N}$ (Stirling formula) and hence

$$\sum_{k=1}^N\ln k\approx\left( N+\frac12\right)\ln N-N+\frac12\ln(2\pi).$$