Simpler expression for $\sum_{k=1}^{n}{k!}$

Question

Is there a way to express $$\sum_{k=1}^{n}{k!}$$ in a simpler way that doesn't use sums up to n ?

I've searched for this around the web and found that the subfactorial function can help with this, however, it's also defined by a sum, so this does not meet the criteria.

Try to have a look here: http://mathworld.wolfram.com/FactorialSums.html — Genadi, Jan 17 '14 at 17:11
For all practical purposes, your sum is approximately equal to its last term. — Lucian, Jan 17 '14 at 17:39

score 0 · Answer 1 · answered Jan 17 '14 at 17:14

0

If you plug it in wolfram Alpha, you get an alternate expression without the subfactorial, but it has the gamma function which by definition is still a sum (integral).

http://www.wolframalpha.com/input/?i=summation+from+1+to+n+of++k+factorial+

answered Jan 17 '14 at 17:14

nicetyartwork

412

It lacks the summation, but is hardly simpler than the given formula. – Lubin Jan 17 '14 at 17:58

Simpler expression for $\sum_{k=1}^{n}{k!}$

1 Answers1