In[]:=
Clear[m,CMRB];
CMRB
=
ReleaseHold[WolframAlpha["20 digtits of the MRB constant",{{"Result",1},"Output"}]]Out[]=
0.1878596424620671203
In[]:=
Plot[{Sum[(-1)^n(n^(1/n)-1),{n,2,40}],CMRB,N[-Sum[(-1)^m/m!Derivative[m][DirichletEta][m],{m,2,x}]+Limit[D[DirichletEta[m],m],m1]],Sum[(-1)^n(n^(1/n)-1),{n,2,x}],Sum[(-1)^n(n^(1/n)-1),{n,2,3}]},{x,1,40},PlotRangeAll,PlotStyle{{DotDashed,Gray},{Thick,Dashed,Red},{ColorData["HTML","MidnightBlue"],Opacity[0.5]},{Yellow,Opacity[0.5]},{Dashed,Green}},PlotLegendsPlaced["Expressions",Right]]
Out[]=