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(*Definethetermsoftheseries*)​​terms=Table[(-1)^n(n^(1/n)-1),{n,1,1000000}];​​​​(*Cumulativesumfunctionthatalternatesbetweenpositiveandnegativ\​​etermstoreachatargetsum*)​​RearrangeToTarget[terms_,target_]:=​​Module[{sum=0,pos=Select[terms,#>0&],​​neg=Select[terms,#<0&],result={}},​​While[Abs[sum-target]>​​0.000001&&(Length[pos]>0||Length[neg]>0),​​If[sum<target,​​If[Length[pos]>0,sum+=First[pos];​​AppendTo[result,First[pos]];pos=Rest[pos]],​​If[Length[neg]>0,sum+=First[neg];​​AppendTo[result,First[neg]];neg=Rest[neg]]];];​​{sum,N[target-sum,20]}]​​​​(*Calculatetherearrangedsumtoreachthetarget*)​​rearrangedSum=RearrangeToTarget[terms,3.1415964]​​
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