Interesting question

[hazy aspen]

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[fresh jewel]

Greatest or least integer?

You can make an inequality on the lower sum, I believe.

[quick garden]

Find the whole part of this

[quick garden]

How

[fresh jewel]

I'm thinking.

[fresh jewel]

I have nothing.

I might have to fetch some theorems I'm not familiar with.

[modest junco]

Aparrently for x>3 we have $\frac{x!}{x-1}<\sum_{i=1}^{x-1}i!<\frac{x!}{x-2}$

looks like i forgot how LaTeX works

[maiden field]

Schlaumau

[modest junco]

and that should be fairly easy to prove with induction

[quick garden]

Thanks