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MRB constant Q

December 11 2011 by Marvin Ray Burns 465
false
Maple

0




Download 10102011.mw


 

As defined at http://mathworld.wolfram.com/MRBConstant.html the MRB constant is

limit(sum((-1)^n*n^(1/n)-1, n = 1 .. 2*N), N = infinity)

.

Download 12102011.mw

However, I have found it surprisingly challenging to compute the simpler

limit(sum(n^(1/n)-1, n = 1 .. N), N = infinity)

,

which seems to diverge:

``

 

evalf(sum(n^(1/n)-1, n = 1 .. 1000))

24.81875537

 (1)

evalf(sum(n^(1/n)-1, n = 1 .. 10000))

43.39893809

 (2)

evalf(sum(n^(1/n)-1, n = 1 .. 20000))

50.02579284

 (3)

 

``
sequence

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