I've been working on this for the past hour, but haven't gone anywhere with it. If anyone can help to complete it, it would be highly appreciated. Thanks

Let 0< a1< b1 and define

an+1= √anbn

bn+1=(an+bn)/2

a) Use induction to show that

an<an+1<bn+1<bn

Thus prove that an and bn converge.

b) Prove that they have the same limit.