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November 22nd, 2015, 06:45 AM   #1
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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.
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November 22nd, 2015, 07:16 AM   #2
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ln(n!)
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November 22nd, 2015, 07:22 AM   #3
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Quote:
Originally Posted by skipjack View Post
ln(n!)
Yes, but it want more simplify it.
I have an approximation from ln(n!)
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November 22nd, 2015, 09:13 AM   #4
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Quote:
Originally Posted by iranch View Post
Yes, but it want more simplify it.
I have an approximation from ln(n!)
You want an approximation formula that doesn't use the factorial function,
correct?
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November 22nd, 2015, 09:54 AM   #5
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Quote:
Originally Posted by Math Message Board tutor View Post
You want an approximation formula that doesn't use the factorial function,
correct?
Thank you,
I can solve the above problem.
But now i can another problem.
I want calculate the below summation:
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November 22nd, 2015, 11:33 AM   #6
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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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