For what value of x is f(x)=x^(1/x) a maximum?
f'(x)=x^(1/x2)(1lnx)=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 $\sum_{n=3}^\infty (1)^n (1n^{1/n})$, URL (version: 20190716): https://math.stackexchange.com/q/3294599






CMRB










Dark Malthorp (https://math.stackexchange.com/users/532432/darkmalthorp), What are some working models that are a fit the formula for the MRB constant?, URL (version: 20200112): https://math.stackexchange.com/q/3505694



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: 7369998 Will 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 supercomputer Processors: Intel Core i99900K (5.0 GHz Turbo) (16Thread) (8Core) 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!

{
< as pointed out by J. Borwein, is the jth 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).
}
.
.
Finch, Steven R. (2003). Mathematical
Constants. Cambridge, England: Cambridge
University Press. p. 450. ISBN 0521818052.
First published in book form by
Gottfried Helms (https://math.stackexchange.com/users/1714/gottfriedhelms), MRB constant proofs wanted, URL (version: 20151224): https://math.stackexchange.com/q/1587347

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)^kk∈Z+=k. and ((k^(1/n)−1)+1)^nn∈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,
following growth, ad infinitum.
Since = 3, consider
Notice this real life application.