In[]:=
$Version
Out[]=
15.0.0 for Microsoft Windows (64-bit) (May 19, 2026)
In[]:=
NSum
n
4
(-1+Zeta[2n])
2
n
,{n,1,Infinity},Method"AlternatingSigns",WorkingPrecision20(*?*)
Out[]=
3.2575668697832447552
In[]:=
NSum
n
4
(-1+Zeta[2n])
2
n
,{n,1,Infinity},Method"AlternatingSigns",NSumTerms10^6,WorkingPrecision20(*?*)
Out[]=
3.2901374073430715359
In[]:=
NSum
n
4
(-1+Zeta[2n])
2
n
,{n,1,Infinity},Method"WynnEpsilon",NSumTerms10^6,WorkingPrecision20(*?*)
Out[]=
3.2901374073430715359
In[]:=
NSum
n
4
(-1+Zeta[2n])
2
n
,{n,1,Infinity},Method"WynnEpsilon",NSumTerms10^6,WorkingPrecision20,PrecisionGoal->10,AccuracyGoal->10(*?*)
Out[]=
3.2901374073430715359
NSum
n
4
(-1+Zeta[2n])
2
n
,{n,1,Infinity},Method"WynnEpsilon",NSumTerms10^7,WorkingPrecision30,PrecisionGoal->15,AccuracyGoal->15(*?looksbetter?*)
Out[]=
3.29978460449113170938379852560
In[]:=
NSum
n
4
(-1+Zeta[2n])
2
n
,{n,1,Infinity},Method{"EulerMaclaurin",Method{"NIntegrate","MaxRecursion"100,Method"DoubleExponential"}}(*?*)
Out[]=
3.28253
(*-------------------------------------------------------------------------------------------*)
In[]:=
Block{$MaxExtraPrecision=50000,M=10000},NTotal@Table
n
4
(-1+Zeta[2n])
2
n
,{n,1,M},20(*youhavetobepatient,ittakessometimetocalculate.,M=10000isnotinfinity!*)
Out[]=
3.3198859427176621682
In[]:=
NSumPolyLog2,
4
k^2
,{k,2,Infinity},WorkingPrecision->20
Out[]=
3.319985938
In[]:=
-2NIntegrate
Log
Sin[Pix]
Pix*(1-x^2)

x
,{x,0,2},WorkingPrecision->20
Out[]=
3.3199859377178288364
In[]:=
2*NIntegrate[(LogGamma[2+x]+LogGamma[2-x])/x,{x,0,2},WorkingPrecision->20]
Out[]=
3.3199859377178288364
In[]:=
NIntegrate
2-4PixyCot[2Pixy]
xy
-
16xy
1-4x^2y^2
,{x,0,1},{y,0,1},WorkingPrecision->23
Out[]=
3.3199859377178288961267