# Thread: Simplifying a sum of factorials

1. ## Simplifying a sum of factorials

How do I simplify $[(n-1)!+(n-2)!+...+1]$

Not sure if this is ext 2, just doing an applied maths problem

2. ## Re: Simplifying a sum of factorials

Originally Posted by BenHowe
How do I simplify $[(n-1)!+(n-2)!+...+1]$

Not sure if this is ext 2, just doing an applied maths problem
There's no easy way to simplify that unless you're willing to use hypergeometric/subfactorial/etc. functions.

WolframAlpha gives:

$(-1)^n\times(n!)\times!(-n-1) - !(-1) - 1$

3. ## Re: Simplifying a sum of factorials

Originally Posted by BenHowe
How do I simplify $[(n-1)!+(n-2)!+...+1]$

Not sure if this is ext 2, just doing an applied maths problem
Let the sum be X

Observe nX = n! + X -1

Then solve for X

4. ## Re: Simplifying a sum of factorials

That's very clever lol. So for stuff like this I have to find how I can re-write the expression to a more useful form/express it in terms of itself?

5. ## Re: Simplifying a sum of factorials

Let the sum be X

Observe nX = n! + X -1

Then solve for X
I don't think it works.
This is not a GS.
nX = n! + n (n-2)! + n (n-3)! + ......

6. ## Re: Simplifying a sum of factorials

Originally Posted by stupid_girl
I don't think it works.
This is not a GS.
nX = n! + n (n-2)! + n (n-3)! + ......
whoops XD

should have picked up on that immediately...

Time to induct

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