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

1. ## 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.

2. My guess is.

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

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

$\log_2(n!)$

3. 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

$\chi$ $\sigma$