(define $pi
  (lambda [$n]
    (/ 4
       (+ 1
          (foldr (lambda [$x $r]
                   (/ (power x 2)
                      (+ (+ (* x 2) 1)
                         r)))
                 0
                 (take n nats))))))

(test (pi 1))
(test (pi 2))
(test (pi 3))
(test (pi 4))
(test (pi 5))
(test (pi 6))
(test (pi 7))
(test (pi 8))
(test (pi 9))
(test (pi 10))
(test (pi 20))
(test (pi 200))

(test (show-decimal 100 (pi 1)))
(test (show-decimal 100 (pi 2)))
(test (show-decimal 100 (pi 3)))
(test (show-decimal 100 (pi 4)))
(test (show-decimal 100 (pi 5)))
(test (show-decimal 100 (pi 6)))
(test (show-decimal 100 (pi 7)))
(test (show-decimal 100 (pi 8)))
(test (show-decimal 100 (pi 9)))
(test (show-decimal 100 (pi 10)))
(test (show-decimal 100 (pi 20)))
(test (show-decimal 100 (pi 200)))

(test (show (rtof (pi 200))))