A Note on The Positivity of the Coefficients of Some Power Series   Expansions
  In this short note, a general result concerning the positivity, under some conditions, of the coefficients of a power series is proved. This allows us to answer positively a question raised by Guo (2010) about the sign of the coefficients of a power series relating the residual errors in Halley's iterations for the $p$th root. 
Omran Kouba
math.CV math.CA