Having trouble with induction proof and limit
Can someone just show me a full blown proof of this problem, I really would have posted everything I had, but its really hard for me to type everything I had. Thanks
Let 0< a1< b1 and define
a) Use induction to show that
Thus prove that an and bn converge.
b) Prove that they have the same limit.
This is what I got so far
1) show it's true for n=1 first.
I derived these an+1=square root of anbn>square root of anan =an
an<an+bn/2<bnanan=an => an<bn+1<bn
I couldn't derive anything for the second term