I don't understand at all how you tell the computer to evaluate a complicated factorial expression such as the one given in in the infinite sum of binomial theorem as Ʃ [n! / k!(n-k)! ] * x^k where n is the final value of the sum and k is where you are in the loop. It's supposed to be INTEGER :: k, n REAL :: sum, fact, x ASK INPUT (what are x and n?) DO k = 0,n sum = sum + fact*x**k fact = fact * (n-k)/(k+1) END DO Is there a procedure to figure out what the term multiplied by the fact variable should be?