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Workingexpansion = 
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  tau/n - (A tau^2)/(27 n^3) - (B tau^3)/(5832 n^5);
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CoefficientList[Workingexpansion, tau][[2]]
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1/n
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Assuming[
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  n ∈ Integers, 
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  TrueQ[Simplify[CoefficientList[Workingexpansion, tau][[2]]] != 0]]
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Assuming[
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 n ∈ Integers,
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 TrueQ[
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  Simplify[
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   CoefficientList[Workingexpansion, tau][[2]] != 0
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   ]
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  ]
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 ]