Solution: Let and be positive numbers with . Let be their arithmetic mean and their
Chapter 11, Problem 91(choose chapter or problem)
Let and be positive numbers with . Let be their arithmetic mean and their geometric mean: Repeat this process so that, in general, (a) Use mathematical induction to show that (b) Deduce that both and are convergent. (c) Show that . Gauss called the common value of these limits the arithmetic-geometric mean of the numbers and .
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