I dont know where you got that formula, it is obviously wrong.
2!=2*1 which does not equal 2*3/2
There must be a confusion somewhere.
Gauss as a small boy in school was told by his teacher to add numbers from 1 to 100, after which he can play outside. While everyone else was still adding away, he went out and played after about 2 minutes. His teacher was about to punish him when he told the teacher he finished!
When asked how he did it, he answered:
Write the numbers 1-100 and 100-1 one on top of the other and add vertically. We have 100 sums of 101 for two rows, so the sum for one row is 101*100/2=5050.
So probably this 1-100 = 5050 formula became the famous Gauss formula, but not for factorial.
If you are looking for an approximation to the factorial function, i.e. f(n)=n! (approximately), use the Stirling formula.
lim n->∞ n!=√(2πn)(n/e)n.
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