On Foias (f) and S
n
of CMRB (m
s
)
In[]:=
x[1,a_]=a;x[n_,a_]:=(1+1/x[n-1,a])^(n-1);f=N[a,32]/.FindRoot[x[220,a]==10^65,{a,1,2},WorkingPrecision->110,MaxIterations->500];
In[]:=
m=NSum[
n
(-1)
(
1/n
n
-1),{n,1,Infinity},WorkingPrecision->32,Method->"AlternatingSigns"];
In[]:=
ms=NSum[
n
(-1)
(
1/n
n
-1),{n,2,10},WorkingPrecision->32,Method->"AlternatingSigns"]+1/2;
In[]:=
t1=
1
π
ms-
523
8747
f
Out[]=
0.187859642462197783744824454371117
In[]:=
t2=m
Out[]=
0.1878596424620671202485195139194
​
In[]:=
t2-t1
Out[]=
-1.306634963049404517×
-13
10