In[]:=
two[n_]:=NSum
16-32k-4
k
(-1)
(4k-3)(16
2
k
-1)
(2k-1)(4k-3)(16
2
k
-1)
,{k,∞},NSumTerms->If[n≠∞,10n,510^6],WorkingPrecision30
In[]:=
two[10000]
Out[]=
2.000000000012499
In[]:=
two[100000]
Out[]=
2.000000000000124999
In[]:=
two[∞]
Out[]=
2.00000000000000499999