Question

Let {a_n} and {b_n}be sequences of positive real numbers such that for n≥1,
a_n+1=1/2(a_n +b_n), b_n+1=sqrt(a_n.b_n)
(a) Show that for n≥2, {a_n} is monotonic decreasing and {b_n}is monotonic increasing.
(b) Deduce that {a_n} and {b_n} have the same limit.
(Hint: Refer to the Arithmetic-Geometric Inequality to get a relation between a_n and b_n)