diff --git a/sicp-ex-1.16.rkt b/sicp-ex-1.16.rkt
index 05b424e..419c02e 100755
--- a/sicp-ex-1.16.rkt
+++ b/sicp-ex-1.16.rkt
@@ -1,3 +1,6 @@
+#! /usr/bin/racket
+#lang racket/base
+
 (define (sqr n)
   (* n n))
 
diff --git a/sicp-ex-1.31.rkt b/sicp-ex-1.31.rkt
new file mode 100644
index 0000000..ebe2f90
--- /dev/null
+++ b/sicp-ex-1.31.rkt
@@ -0,0 +1,27 @@
+#! /usr/bin/racket
+#lang racket/base
+
+(define (product term a next b)
+  (define (iter a result)
+    (if (> a b)
+      result
+      (iter (next a) (* (term a) result))))
+  (iter a 1))
+
+(define (numerator pre-applying n)
+  (* pre-applying (product (lambda (x) (* x x)) 4 (lambda (x) (+ x 2)) n)))
+
+(define (denominator pre-applying n)
+  (* pre-applying (product (lambda (x) (* x x)) 3 (lambda (x) (+ x 2)) n)))
+
+(define (fourth-of-pi n)
+  (cond ((< n 1) 0)
+        ((even? n) (/ (numerator (* 2 (+ n 2)) n)
+                      (denominator 1 ( + n 1))))
+        (else (/ (numerator 2 (+ n 1))
+                 (denominator (+ n 2) n)))))
+
+(fourth-of-pi 1)
+(fourth-of-pi 2)
+(fourth-of-pi 3)
+(fourth-of-pi 60)