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guess or proof?

just kidding.

guess is welcome too :D

Good guess!! :D

closed form i mean.

won't post until i prove it.

alrighty!

Yes, I think it works. We just need to show more rigorously that
\[\lim_{n\to\infty}\frac{(n-r)\cdot(n-r)!}{n\cdot n!}=0\]
for all \(0

yeah, I'm looking at that now actually ;)

actually just showing it works for r=1 will show it for the rest

Agree :).

I found it

i think it is just \[\frac{(n+1)!-1}{(n+1)!}\]yes?

Awesome satellite! :D

proof by induction as soon as i figure it out.

My method doesn't work?

Oh I see

well actually satellite has not shown anything. i just said it.

so no credit yet that is for sure.

Fun problem though

any hints?

Are you sure you want a hint. I am afraid it will soil the fun :).

Just factor

ok no hint. perhaps induction is not way to go?

oh lord i get the dumb guy award

ok, half hint. The summation on the top can be made into a telescoping sum.

hehe.. sometimes we can't see the forest for the trees. Happens to us all.

polpak got it. proof by induction done.

but now i have to think about the telescope.

\((n+1)!-1=(n+1)!-1!\) :D

I think a hint won't hurt now :D.
\(n\cdot n!=((n+1)-1)\cdot n!\)