9. Let 0 < Yl < Xl and set Xn +Yn Xn+l = 2 and Yn+l = v'xnYn, nEN.

(a) Prove that 0 < Yn < Xn for all n E N.

(b) Prove that Yn is increasing and bounded above, and Xn is decreasing and bounded below.

(c) Prove that 0 < Xn+l - Yn+l < (Xl - Yl)/2n for n E N.

(d) Prove that limn->oo Xn = limn->oo Yn. (This common value is called the arithmetic-geometric mean of Xl and Yl.)