

Subject:
Approximate or Compute a finite harmonic series
Category: Science > Math Asked by: tc2cityga List Price: $5.00 
Posted:
05 Nov 2006 06:17 PST
Expires: 05 Dec 2006 06:17 PST Question ID: 780243 

There is no answer at this time. 

Subject:
Re: Approximate or Compute a finite harmonic series
From: emollga on 05 Nov 2006 07:07 PST 
You can get a good approximation by calculating ln n + .5772. The larger n is, the better the approximation. (ln n is the natural, or basee, logarithm of n; .5772 is the approximate value of gamma, or Euler's Constant, which is the limit, as n increases without bound, of the sum of the series 1+1/2+1/3+...+1/nln n.) For your example with n = 75, the calculation evaluates to about 4.895, which is reasonably close to your value of 4.901. 
Subject:
Re: Approximate or Compute a finite harmonic series
From: emollga on 06 Nov 2006 14:44 PST 
The formula below gives an even better approximation: sum = ln n + gamma + 1/(2n)  1/(12n^2) + 1/(120n^4) ... The formula above was found at: http://en.wikipedia.org/wiki/EulerMascheroni_constant Here is gamma to 45 decimal places, from the same webpage: ? ? 0.57721 56649 01532 86060 65120 90082 40243 10421 59335 
If you feel that you have found inappropriate content, please let us know by emailing us at answerssupport@google.com with the question ID listed above. Thank you. 
Search Google Answers for 
Google Home  Answers FAQ  Terms of Service  Privacy Policy 