Consider  S=sum((-1)^n*(n^(1/n)-a),n=1..infinity).
S=1/2*(a+2m-1), where m is the MRB constant.

Let m = MRB constant = sum((-1)^n*(n^(1/n)-1),n=1..infinity)

Notice the sequential patterns Maple gives for an output to the following:

Digits := 96; floor(evalf((10^100+1)*(1/9801)))

which gives 1020304050607080910111213141516171819202122232425262728293031323334353637383940414243444546474850

and

evalf((10^100+1)*(1/9801)-floor((10^100+1)*(1/9801)))

which gives 0.505254565860626466687072747678808284868890929496990103050709111315171921232527293133353739414345

.

In honor of Pi Day, in this blog I would like to show that the MRB constant has some meaning in our day to day lives. The first two messages are lifted from a discussion group.

In this blog we will consider what happens when the formula for the MRB constant is iterated infinitely. This will invoke divergent series, but we will use an analytic extension of the formula to continue our iterating. We will also find a new use for MRB2=1-2*MRB constant.( Sloane's A173273 )

I think Maple should emphasize occupational and problem specific packages, like its TA software for teachers. Maple should have a package or set of packages for each type of engineer: electrical,hydrological, etc. Actually, Maple should promote packages for all professions that tend to need it. An abundance of packages would enable many new users to benefit from the power of maple with the experience of the advanced users who helped develop the packages.