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I've been looking into two very specific forms that are related to the MRB constant$\sum _{n=1}^{\infty } (-1)^n \left(n^{\frac{1}{n}}-1\right)$ cf http://mathworld.wolfram.com/MRBConstant.html.

They are

$\sum _{n=1}^{\infty } (-1)^n \left(n^{\frac{u}{n}}-1\right)$ and $\sum _{n=1}^{\infty } (-1)^n \left(n^{\frac{u}{n}}-u\right)$.
I've had some minor success as you can see at http://www.mapleprimes.com/posts/104016-A-Very-False-Graph .

As the amateur that I amhoping that some of you with research experience could help me come up with , I would like to ask academic (or otherpossible questions concerning those ) professionals if they have ever come across these formsthat , or are they clearly localized? To see where I could look into and add to my investigation. The MRB constant is defined in Mathworld at http://mathworld.wolfram.com/MRBConstant.htmlget these two forms you can cf http://www.mapleprimes.com/posts/104016-A-Very-False-Graph.

Post Closed as "not a real question" by Todd Trimble, Andres Caicedo, J.C. Ottem, Gjergji Zaimi, Charles Matthews
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# Two Specific sets of Sums

I've been looking into two very specific forms that are related to the MRB constant. They are

$\sum _{n=1}^{\infty } (-1)^n \left(n^{\frac{u}{n}}-1\right)$ and $\sum _{n=1}^{\infty } (-1)^n \left(n^{\frac{u}{n}}-u\right)$.
I've had some minor success as you can see at http://www.mapleprimes.com/posts/104016-A-Very-False-Graph . I am hoping that some of you with research experience could help me come up with other possible questions concerning those forms that I could look into and add to my investigation. The MRB constant is defined in Mathworld at http://mathworld.wolfram.com/MRBConstant.html .