Arithmetic-geometric mean

In mathematics, the arithmetic-geometric mean (AGM) of two positive real numbers x and y is defined as follows.First compute the arithmetic mean of x and y and call it a1. Next compute the geometric mean of x and y and call it g1; this is the square root of the product xy:a1 = (x + y) / 2 g1 = √(xy).Then iterate this operation with a1 taking the place of x and g1 taking the place of y. In this way, two sequences (an) and (gn) are defined:
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