Let a and b be positive numbers with a>b. Let a1 be their arithmetic mean and b1 their geometric mean. a1 = a+b/2      b1 = √ab Repeat this process so that, in general, an+1= an+bn/2     bn+1= √ab (a) Use mathematical induction to show that an>an+a>bn+1>bn (b) Deduce that both {an} and {bn} are convergent. (c) show that limn-->infinity an = limn-->infinity bn. Guass call the commone value of thes limits the arithmetic-geometric mean of the numvers a and b.

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