MaplePrimes - comments on Post, MRB constant Q

MaplePrimes - comments on Post, MRB constant Q http://www.mapleprimes.com/posts/128614-MRB-Constant-Q en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Fri, 12 Jun 2026 21:17:10 GMT Fri, 12 Jun 2026 21:17:10 GMT The latest comments added to the Post, MRB constant Q http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, MRB constant Q http://www.mapleprimes.com/posts/128614-MRB-Constant-Q   The limit(sum(n^(1/n http://www.mapleprimes.com/posts/128614-MRB-Constant-Q?ref=Feed:MaplePrimes:MRB constant Q:Comments#comment128647     From the following emperical evidence alone it appears that the limit(sum(n^(1/n)-1, n = 1 .. N), N = infinity) just might converge. Here is a table of limits x    limit(sum(n^(1/n)-1,n=1..N),N=10^x) 1      3.1511647323226333 2     11.452637624960385 3     24.818755742523738 4     43.39893188518323 5     67.26154566874983 6     96.42261224741904 7     130.8850394120835 8     170.649287381816 9     215.7154228449 10   266.08345507 11   321.7533848 12   382.725223 13   448.99902 14   520.57333 15   597.45191 16   679.63721 17   767.0216 18   829.7285 19   829.727 20   829.809 21   829.71 22   829.71 23   829.71 24   829.71 25   829.71 26   829.71 27   829.71 28   829.71 The table is from Mathematica using the following code: Table[{x,NSum[n^(1/n)-1,{n,1,10^x}, Method ->{"EulerMaclaurin", Method->{"NIntegrate", "MaxRecursion"->20, Method->"DoubleExponential"}}]},{x,28}]      The latest comments added to the Post, MRB constant Q 128647 Mon, 12 Dec 2011 04:10:26 Z Marvin Ray Burns Marvin Ray Burns I believe the previous table simply shows http://www.mapleprimes.com/posts/128614-MRB-Constant-Q?ref=Feed:MaplePrimes:MRB constant Q:Comments#comment128809 I believe the previous table simply shows some "maxing out" of the software instead of showing convergence of the limit(sum(n^(1/n)-1, n = 1 .. N), N = infinity).      <a href="http://marvinrayburns.com">marvinrayburns.com </a> The latest comments added to the Post, MRB constant Q 128809 Thu, 15 Dec 2011 05:38:05 Z Marvin Ray Burns Marvin Ray Burns sum(n^(1/n)-1, n = 1 .. infinity) diverges because n^ http://www.mapleprimes.com/posts/128614-MRB-Constant-Q?ref=Feed:MaplePrimes:MRB constant Q:Comments#comment129068 sum(n^(1/n)-1, n = 1 .. infinity) diverges because n^(1/n) - 1 > exp(1/n) - 1 for n >= 3 and limit((exp(1/n) - 1)/(1/n), n = infinity)=1. Therefore, sum(exp(1/n)-1, n = 1 .. infinity) diverges and so does sum(n^(1/n)-1, n = 1 .. infinity).    The latest comments added to the Post, MRB constant Q 129068 Sun, 25 Dec 2011 04:14:37 Z Marvin Ray Burns Marvin Ray Burns