Let on :5 on 2*; and consider the arithmetic and geometric means at = an+bu- bl = tat-lobe '2 Continue this by iteration by setting :1 +b n+1 = 2 \"1- b+l = '1an- (a) Start the sequence with no : 2 and b0 : 1 and generate the rst 5 terms of {an} and {bu}. Do you see convergence? (1)) Use inathelnnticel induction to show that o" > an\" > b\" :a- by, 1. (c) Hence show that hoth {on} and {on} are convergent. (d) Show using the method of 2{e) that the limits of the sequences {on} and {on} are equal