Math Problems

Let me know if you can work any of the following.

1. Let a and b be any two positive numbers. Let a₀=a and b₀=b. Define the following sequence of numbers a_n+1=[a_n+b_n]/2, b²_n+1=a_nb_n Show that each of these sequences is monotone, and that they converge to a common limit.
2. Suppose Adam buys one dollar's worth of flour each week and Eve buys one pound of flour each week. If the price of flour is not constant from week to week, which one gets the lowest average cost per pound of flour?