what is the units digit of the sum of 1!+2!+3! ... n! when n=2019. Include an explanation and what a unit digit is.

Hey!

Finding the factorial for the first few numbers, we have:

1!=1

2!=2

3!=6

4!=24

5!=120

6!=720

7!=720*7

8!=720*56

What we can see as a clear pattern from 5! and on is that our number ends with a 0, making the units digit 0. Therefore, when we add the units digit of 5! and on, we have a result of 0. So, we can simply add the units digits of 1!, 2!, 3!, and 4!, which is 1+2+6+4=13. Since the units digit is the last number, we can drop the tens place to get an answer of 3.

Feel free to ask further questions!