November 22nd, 2015, 06:45 AM  #1 
Newbie Joined: Nov 2015 From: japan Posts: 15 Thanks: 0  Simplify sum
Hello, Would you mind tell me ,how can simplify it? please Ln(x) or log(x) doesn't matter for me. I should use the integral or Stirling's approximation. with your opinion, which of these is simpler? Could you simplify it with Stirling's approximation? Thanks Last edited by iranch; November 22nd, 2015 at 06:59 AM. 
November 22nd, 2015, 07:16 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 21,020 Thanks: 2256 
ln(n!)

November 22nd, 2015, 07:22 AM  #3 
Newbie Joined: Nov 2015 From: japan Posts: 15 Thanks: 0  
November 22nd, 2015, 09:13 AM  #4 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  
November 22nd, 2015, 09:54 AM  #5 
Newbie Joined: Nov 2015 From: japan Posts: 15 Thanks: 0  
November 22nd, 2015, 11:33 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 21,020 Thanks: 2256 
lg(n!) = ln(n!)/ln(2), where lg denotes the base 2 logarithm. It's hard to say what is simplest, as you haven't defined "simplest" or stated what accuracy is needed. 

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