Thread: simplify (factorial expression)

x! - [(x-1)!+(x-2)!+(x-3)!...............2!+1!]

Intuitive guess, based on 5:
expression is 5*4*3*2*1 - 4*3*2*1 - 3*2*1 - 2*1 - 1 = 4*4*3*2*1 - 3*2*1 - 2*1 - 1 = 4*3*2*2*1 etc.

So I think the answer is going to be (x-1)!, though that's not a formal proof.

Originally Posted by Annatala

Intuitive guess, based on 5:
expression is 5*4*3*2*1 - 4*3*2*1 - 3*2*1 - 2*1 - 1 = 4*4*3*2*1 - 3*2*1 - 2*1 - 1 = 4*3*2*2*1 etc.
So I think the answer is going to be (x-1)!, though that's not a formal proof.

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If for then we get for the first five of those.

I have not seen a pattern yet.

See also the MathWorld article on the sum of factorials.

Originally Posted by emakarov

See also the MathWorld article on the sum of factorials.

Also looking at this sequence site we see that this does not to yield much.

do v have any other expression for sum of factorial ??

may be we can find a range (in terms of n) in which the answer would lie..

I ll try this now...

Originally Posted by livinggourmand

do v have any other expression for sum of factorial ??
may be we can find a range (in terms of n) in which the answer would lie..I ll try this now...

I have no idea what that post says.
If you follow the link in post #5, it is clear that the folks at ATT labs do not know of any simplification of this sequence.

Ah, I figured out the mistake in my quickie guess-calculation.

a * b * c - b * c = (a-1) * b * c is true, but a * b * c - c = (a * (b-1) * c) is false. It should = ((a * b) - 1) * c, which doesn't simplify and gets worse the longer the expression is.