Let
(a) Show that
(b) Use Exercise 50 to show that
(c) Use parts (a) and (b) to show that
and deduce that
(d) Use part (c) and Exercises 49 and 50 to show that
This formula is usually written as an infinite product:
and is called the Wallis product.
(e) We construct rectangles as follows. Start with a square of area 1 and attach rectangles of area 1 alternately beside or on top of the previous rectangle (see the figure). Find the limit of the ratios of width to height of these rectangles.
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