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

(test (pi 5))
(test (rtod' (pi 5)))
(test (show-decimal' (pi 5)))
(test (pi 6))
(test (rtod' (pi 6)))
(test (show-decimal' (pi 6)))
(test (pi 7))
(test (show-decimal 10 (pi 7)))
(test (pi 100))
(test (rtof (pi 100)))
(test (show-decimal 100 (pi 100)))