factorial is cool

So to find the unit digit v will start with 1! 1!=1 2!=2 3!=6 4!=24 5!=120 All other (to infinity) eill have 0 as their unit digit So unit digit =1+2+6+4=3

n! = n(n-1)(n-2)(n-3)...(3)(2)(1).

5! has a 2 factor and a 5 factor, so it will end in a 0. Every factorial after 5! is just a multiple of 5! and thus will end in a 0. So after 4!, every factorial will end in a 0.

So we only need to add the units digits of 1!, 2!, 3! and 4!.

1!+2!+3!+4! = 1+2+6+24= 33, last digit is 3.

Thus, the units digit of 1!+2!+3!+4!------infinity! is 3.