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In this short note, a general result concerning the positivity, under someconditions, of the coefficients of a power series is proved. This allows us toanswer positively a question raised by Guo (2010) about the sign of thecoefficients of a power series relating the residual errors in Halley'siterations for the $p$th root.

A Note on The Positivity of the Coefficients of Some Power Series Expansions