## Two Specific sets of Sums [closed]

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

They are

$\sum _{n=1}^{\infty } (-1)^n \left(n^{\frac{u}{n}}-1\right)$ and $\sum _{n=1}^{\infty } (-1)^n \left(n^{\frac{u}{n}}-u\right)$.

As the amateur that I am, I would like to ask academic (or other) professionals if they have ever come across these forms, or are they clearly localized? To see where I get these two forms you can cf http://www.mapleprimes.com/posts/104016-A-Very-False-Graph.

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So, the question is to come up with other questions? And how will it be judged whether the questions we come up with are the right questions? Please have a look at the faq and see whether you think your question is suitable for this site. – Gerry Myerson Apr 12 2011 at 5:43
This is my first time to know about the MRB constant，does it play a very important part in number theory? – yaoxiao Apr 12 2011 at 6:26
Is MRB your acronym? Anyway, maybe start by asking yourself why you are interested in that series, and what you are looking for. – Pietro Majer Apr 12 2011 at 7:38
I think that "in which problems does this series come up?" is a legitimate question. Voting to reopen. – algori May 31 2011 at 3:53