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Sum and NSum problem


Mathrematica v7

1) Resulting function resturns k

Sum[(x^k/k!)^k, {k, 1, Infinity}]

-(x^k/(x^k - k!))



2)NSum worses the approximation of zeta function

eexp[x_, n_: 30] :=
  1 + Sum[(x)^k/k!, {k, 1, n}]; (*exponential function definition*)


nzzeta[s_] := NSum[eexp[-s Log[k]], {k, 1, 60}];

nzzeta[2]

75.3061

zzeta[s_] := Sum[eexp[-s Log[k]], {k, 1, 60}];

zzeta[2.]

1.62842

Zeta[2.]

1.64493

Are these examples bugs? thanks


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