rc,rcdecreases on some interval[0,]and thusrc( ) <r. On the other hand, underthe assumptions listed in(4), the condition 0≤r≤Dis sufficient but not necessaryfor the conclusion that forsomevalues ofp∈(0,1),rc>r. For example, for thegeneralized FPP Problem withp=q=1/2 and thusλ=1/4, the right side of(3)is4/(81)[7+√130].=.909. Thus if(56/65) <r<4/(81)[7+√130], thenrc(1/4) >reven thoughr>D.References1. D. Freedman, R. Pisani, and R. Purves,Statistics, 3rd ed., W. W. Norton, New York, 1998.◦On the Remainder in the Taylor TheoremLior Bary-Soroker ([email protected]), Einstein Institute of Mathematics, TheHebrew University, Jerusalem 91904, Israel, and Eli Leher ([email protected]),School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israeldoi:10.4169/074683409X475706We give a short straightforward proof for a bound on the reminder term in the Taylortheorem. The proof uses only induction and the fact thatf≥0 implies the mono-tonicity off, so it might be an attractive proof to give to undergraduate students.Letfbe ann-times differentiable function in a neighborhood ofa∈R. Recall thatthe Taylor polynomial of ordernoffatais the polynomialPn(x)=f(a)+f(a)(x−a)+ · · · +f(n)(a)n!