Section 11.3, #36, p. 745

S10=N[Sum[1/n^4,{n,10}]]

{S10+NIntegrate[1/x^4,{x,11,Infinity}],S10+NIntegrate[1/x^4,{x,10,Infinity}]}

S=N[Pi^4/90]

Nmin=Ceiling[(1/(3*.00001))^(1/3)]