Oh! Sorry, I transcribed the question erroneously. It should be:
Given x0 and y0 such that x0 > y0 > 0. Define, for n = 0,1,2,,
xn+1 =(xn +yn)/2 , yn+1 = 2xnyn/(xn + yn) .Find the limits of {xn} and {yn}.
why is the answer lim{xn} = lim{yn} = sqrt(x0y0)?