# Fortran Factorials

by Goatsenator
Tags: factorials, fortran
 P: 20 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?
 Engineering Sci Advisor HW Helper Thanks P: 7,285 Look at what the term are summing, for each value of k. When k = 0, it is n! / (0! n!) so k0 = 1 When k = 1, it is n! / (1! (n-1)! so k1 = n = k0 * n / 1 When k = 2, it is n! / (2! (n-2)! so k2 = n(n-1) / 2! = k1 * (n-1) / 2 When k = 3, it is n! / (3! (n-3)! so k3 = n(n-1)(n-2) / 3! = k2 * (n-2) / 3 etc. That is what the program is doing when it updates "fact".
 P: 20 Hmmm... then fact * (n-k)/(k+1) can't be right because it doesn't match the results of working out all the factorials like that. I checked it in command prompt and it said the sum with x = 2 and n = 2 is 5. This sum represents (1+x)^n which should be 9 in that case. I thought fact * ( (n-k+1) / k ) would work but I'm not getting the right answer with that either.
 P: 20 Fortran Factorials disregard that. i worked it out on paper and i got 9 but for some reason the program is outputting 5... If the k0,k1,k2 etc values are the "fact", how is (n-2)/3 = (n-k)/(k+1) for k = 3? That's why I thought it should be ( (n-k+1) / k ).
Engineering
HW Helper
Thanks
P: 7,285
 Quote by Goatsenator If the k0,k1,k2 etc values are the "fact", how is (n-2)/3 = (n-k)/(k+1) for k = 3? That's why I thought it should be ( (n-k+1) / k ).
The code calculates "k3" when k = 2, not when k = 3.

Each time through the loop, it uses the current value of fact, then calculates the next value.
 P: 129  i=n fact=1 sum=1 DO k= 1,n f = f*i/k*x i = i-1 s = s + f END DO
P: 20
 Quote by AlephZero The code calculates "k3" when k = 2, not when k = 3. Each time through the loop, it uses the current value of fact, then calculates the next value.
OH! I just realized that! It's so simple now that I understand it. Thank you for the help!

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