(1000!-999!-998!)/(1000!+999!+998!)=
998!(1000*999-999-1)/998!(1000*999+999+1)=
(1000*999-1000)/(1000*999+1000)=
(1000*998)/(1000*1000)=998/1000 and u can simplify this number
I have no idea how you would do this problem: Express this expression as a rational number in lowest terms.
(1000!-999!-998!)/(1000!+999!+998!)
4 answers
You have to realize that factorials can be written in several ways
e.g.
12! = 12*11*10*9! or
12! = 12*10*10! I am saying you can stop anywhere
(1000!-999!-998!)/(1000!+999!+998!)
= (1000*999*998!-999*998!-998!)/(1000*999*998!+999*998!+998!)
=998!(1000*999-999-1)/[998!(1000*999+999+1)]
= 998000/1000000
=499/500
e.g.
12! = 12*11*10*9! or
12! = 12*10*10! I am saying you can stop anywhere
(1000!-999!-998!)/(1000!+999!+998!)
= (1000*999*998!-999*998!-998!)/(1000*999*998!+999*998!+998!)
=998!(1000*999-999-1)/[998!(1000*999+999+1)]
= 998000/1000000
=499/500
Both numerator and denominator have a common factor of 998!. Cancel that out and you have
[1000*999 -999-1]/[1000*999 + 999+1]
=[1000(999-1)]/[1000(999+1)]
=449/500
[1000*999 -999-1]/[1000*999 + 999+1]
=[1000(999-1)]/[1000(999+1)]
=449/500
499/500