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Variations to the MRB constant

As some of you know now, the MRB constant is computed by the convergent Sum[(-1)^n*(n^(1/n) - 1), {n, 1, Infinity}] .

I wondered what happens when you get the expression all mixed up and write Sum[(-1)^n ((1/n)^(n - 1)), {n, 1, Infinity}] ?

You get another convergent series! It is = -0.596965555578...

What can be said about that? `

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