Let a and b be positive numbers with a . b. Let a1 be their arithmetic mean and b1 their
Chapter 11, Problem 91(choose chapter or problem)
Let a and b be positive numbers with a . b. Let a1 be their arithmetic mean and b1 their geometric mean: a1 a 1 b 2 b1 sab Repeat this process so that, in general, an11 an 1 bn 2 bn11 san bn (a) Use mathematical induction to show that an . an11 . bn11 . bn (b) Deduce that both han j and hbn j are convergent. (c) Show that limnl` an limnl` bn. Gauss called the common value of these limits the arithmetic-geometric mean of the numbers a and b
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer