Fortran Factorials

1. Feb 9, 2012

Goatsenator

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?

2. Feb 9, 2012

AlephZero

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".

3. Feb 9, 2012

Goatsenator

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.

4. Feb 9, 2012

Goatsenator

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 ).

Last edited: Feb 9, 2012
5. Feb 10, 2012

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.

6. Feb 10, 2012

Xitami

Code (Text):
i=n
fact=1
sum=1
DO k= 1,n
f = f*i/k*x
i = i-1
s = s + f
END DO

7. Feb 10, 2012

Goatsenator

OH! I just realized that! It's so simple now that I understand it. Thank you for the help!