Marvin Ray Burns

 I've been using Maple since 1997 or so.

MaplePrimes Activity


These are Posts that have been published by Marvin Ray Burns



Download 10102011.mw


 

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

 

The MRB constant =    sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity)

 

Concerning the following divergent and convergent series, we see that

sum((-1)^n*(n^(1/n)-x), n = 1 .. infinity)=

 

Here is the progress made in the investigation of what I call the convergents constants:
https://oeis.org/wiki/Table_of_convergents_constants

I wonder if anyone would be interested in adding anything to it. I would like to see the convergents constants studied some in Maple to compare with my Mathematica results; my investigation is in dire need of some proof other than my...

I've made a little progress in definig a new set of constants from the generalized continued fraction that I mentioned in my previos post.

 

See https://oeis.org/wiki/Convergents_constant.

Since -1 = i^2 I thought that there could be some meaning behind "alternating" series that instead of beginning with (-1)^n begin with (a+b*i)^n, with real coefficients, for abs(a)<1 and abs(b)<1. I'm not sure but it seems that such series are absolutely convergent, because (a+b*i)^n -> 0+0I as n->infinity, hence the term utterly diminishing series instead of alternating series.

As an example,
Where sum((-1)^n*(n^(1/n)-1),n=1..infinity)= 0.187859642462067120248... ,

4 5 6 7 8 9 10 Last Page 6 of 14