it follows that
For what value of x is f(x)=x^(1/x) a maximum?

f'(x)=x^(1/x-2)(1-lnx)=0,

x=e and gives a maximum of e^(1/e)=1.444667861...

 user90369 (https://math.stackexchange.com/users/332823/user90369), High precision evaluation of the series $\sum_{n=3}^\infty (-1)^n (1-n^{1/n})$, URL (version: 2019-07-16): https://math.stackexchange.com/q/3294599
 where A is the Glaisher-Kinkelin constant.
 formulas (11)+(16)+(19).
 CMRB
 Dark Malthorp (https://math.stackexchange.com/users/532432/dark-malthorp), What are some working models that are a fit the formula for the MRB constant?, URL (version: 2020-01-12): https://math.stackexchange.com/q/3505694
 where  η is the Dirichlet eta function. Both should be valid for all z∈C..
 CMRB
 5,555,555 digit computation of CMRB(MRB supercomputer output at 18:50:08 am EDT  |  Friday, July 3, 2020) Start time is Fri 19 Jun 2020 22:20:08.Iterations (iter.) required: 7369998Will give 3599 time estimates, each more accurate than the previous.Will stop at 7370752 iterations to ensure precision of around 5583332 decimal places...1132544 iter. done in 1.161*10^6 s. Ave. 0.97566iter./s. Should take 87.429 days or 7.554*10^6s. Finish Tue 15 Sep 2020 08:37:29.{15.3654,% done.}MRB supercomputerProcessors: Intel Core i9-9900K (5.0 GHz Turbo) (16-Thread) (8-Core) 3.6 GHz. CPU Boost: Stage 2: Overclock CPU - Up to 5.1GHz on All CPU Cores at 3200 Mhz RAM Extreme Cooling: H20: Stage 2: Corsair H115i PRO - 280mm Liquid CPU Cooler  with the following two exterior nodes: 4.7 GHz on all Intel 6 cores at 3000 MHz RAM and 4 cores of 3.6 GHz at 2400 MHz RAM!
<- by Fubini’s theorem for double series along with->
{
<- by a Taylor expansion of η(s) around s = 0
<- as pointed out by J. Borwein,         is the j-th Taylor
coefficient in the expansion of             about x = 0.
This conditionally convergent series is transformed
into the following
absolutely convergent two by
Richard Crandall (2012).
}
These limits are transformed into the
following
infinite series.
Collecting the terms of this series gives us
the following
conditionally convergent one.
.
.
(η is the Dirichlet eta function.)
Finch, Steven R. (2003). Mathematical
Constants. Cambridge, England: Cambridge
University Press. p. 450. ISBN 0-521-81805-2
.
First published in book form by
 Gottfried Helms (https://math.stackexchange.com/users/1714/gottfried-helms), MRB constant proofs wanted, URL (version: 2015-12-24): https://math.stackexchange.com/q/1587347
 CMRB = =CMRB
 ,
 =
 =
 =
 =
 =
 CMRB
Given that C MRB =
.

The MRB constant is defined at http://mathworld.wolfram.com/MRBConstant.html. After a lot of looking I found a
connection between the MRB constant and applied math:

The MRB constant is ∑(−1)^k(k^(1/k)−1), and that k^(1/k)−1 is the interest rate to multiply an investment k times in
k periods -- as well as other growth models involving the more general expression (1+k)^n --
since ((k^(1/k)−1)+1)^k|k∈Z+=k. and ((k^(1/n)−1)+1)^n|n∈Z+=k.

We can say, the result of summing, with alternating signs, the interest rate to multiply an investment k times in k
periods (or the equivalent growth model) could be the end "growth" rate resulting from growth, following decay,