Consider flipping n fair coins. Let Hₙ be the total number of heads, and let Fₙ be the number of heads on coins 1 through n-1 (i.e., omitting the nth coin). Let
xₙ=Hₙ/Hₙ+1, and Yₙ=Fₙ/Hₙ+1, and z=0. prove that Xₙ-Yₙ → Pz