MaplePrimes - comments on Post, MRB Constant I

MaplePrimes - comments on Post, MRB Constant I http://www.mapleprimes.com/posts/81003-MRB-Constant-I en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Sat, 13 Jun 2026 02:11:00 GMT Sat, 13 Jun 2026 02:11:00 GMT The latest comments added to the Post, MRB Constant I http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, MRB Constant I http://www.mapleprimes.com/posts/81003-MRB-Constant-I Any value for S may be achieved from S=sum((-1)^k (k^(1/k) - a). http://www.mapleprimes.com/posts/81003-MRB-Constant-I?ref=Feed:MaplePrimes:MRB Constant I:Comments#comment81494 The point of my laat message was, S=sum((-1)^k (k^(1/k) - a),k=1..infinity)=1/2*(a+2m-1) where m is the MRB constant. So I conclude as follows: S=1/2*(a+2m-1). Thus, a=2S+(1-2m) where 1-2m is MRB2, the solution for a in sum((-1)^k (k^(1/k) - a),k=1..infinity)=0. So, like m is achieved from sum((-1)^k (k^(1/k) - a),k=1..infinity) with a=1, any value for S may be achieved from S=sum((-1)^k (k^(1/k) - a),k=1..infinity); the value for a needed is simply 2S+MRB2. In these series the sum is the numerical value which is arrived at according to principles of analysis.<a href="http://marvinrayburns.com"> </a> The latest comments added to the Post, MRB Constant I 81494 Mon, 26 Apr 2010 02:43:24 Z Marvin Ray Burns Marvin Ray Burns sum((-1)^k*(k^(1/k)-a),k = 1 .. infinity) = m+(a-1)/2 http://www.mapleprimes.com/posts/81003-MRB-Constant-I?ref=Feed:MaplePrimes:MRB Constant I:Comments#comment81260 <img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=813ae2add3b62a759cbafcd3fe84240d.gif" alt="sum((-1)^k*(k^(1/k)-a),k = 1 .. infinity)">  =  <img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=39934ca5fed65b93041c625636a5ad6a.gif" alt="m+(a-1)/2">, where m is the MRB constant which is, <img class="math" src="http://www.mapleprimes.com/MapleImage.ashx?f=916937fc0dd08291425510ca67f901c3.gif" alt="sum((-1)^k*(k^(1/k)-1), k = 1 .. infinity)">: See the previous messages.   Levin's u-transform assigns values to divergent series.   <a href="http://marvinrayburns.com">marvinrayburns.com </a> The latest comments added to the Post, MRB Constant I 81260 Mon, 26 Apr 2010 02:44:33 Z Marvin Ray Burns Marvin Ray Burns MRB constant K http://www.mapleprimes.com/posts/81003-MRB-Constant-I?ref=Feed:MaplePrimes:MRB Constant I:Comments#comment88311 Since the MRB constant is an alternating sum of all integers to their own roots, f(n)=(-1)^n* n^(1/n); a thorough understanding of the changes in f, as n changes, is important. So this will be covered in a future blog <a href="http://www.mapleprimes.com/blog/marvinrayburns/mrbconstantk">MRB constant K</a>. The latest comments added to the Post, MRB Constant I 88311 Fri, 21 May 2010 19:42:35 Z Marvin Ray Burns Marvin Ray Burns