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# What is 1000!-999!

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What is 1000!-999!

Guest Oct 22, 2014

#5
+93691
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So it is Heureka.

I had to think about that one  :))

$$\\99.9\% \;\;of\;\;1000!\\\\ =\frac{999}{1000}*1000!\\\\ =\frac{999}{1000}*1000*999!\\\\ =999*999!\\\\$$

Melody  Oct 22, 2014
#1
+90056
+5

Notice that

n! - (n -1 ) !   =

[n x (n-1) x (n-2) x.......x 3 x 2 x 1 ]  - [ (n-1) x (n-2) x.......x 3 x 2 x 1 ]

And factoring out the common term, we have

[ (n-1) x (n-2) x.......x 3 x 2 x 1 ] [n  - 1]  =

[n-1]! * [n-1]

So....... 1000! - 999! =

999! * (999)       ......whatever that is !!!  (it's huge, to be sure)

CPhill  Oct 22, 2014
#2
+93691
+5

Chris is of course correct.  He just makes it look hard LOL

1000!=999!x1000

so

1000!-999!

= 999!x1000 - 999!x1

I can factor out the 999!

=999!(1000-1)

=999! x 999

Melody  Oct 22, 2014
#3
+90056
0

It's math....it's supposed to look hard......if it looked easy.......the questioners would be on to us!!!!! LOL!!!

CPhill  Oct 22, 2014
#4
+20033
+5

What is 1000!-999!  Its 99.9% of 1000!

= 4.0198487281701667977015873148908e+2567

heureka  Oct 22, 2014
#5
+93691
+8

So it is Heureka.

I had to think about that one  :))

$$\\99.9\% \;\;of\;\;1000!\\\\ =\frac{999}{1000}*1000!\\\\ =\frac{999}{1000}*1000*999!\\\\ =999*999!\\\\$$

Melody  Oct 22, 2014
#6
+20033
+5

Very fine Melody!

heureka  Oct 22, 2014