easy problem

$5! = 120$

$6! = 720$

In general,after $5!$ ,units digit is zero.

Therefore we have to just calculate the sum of $1! + 2! + 3! + 4!$ and find the units digit which is $\boxed {3}$

until 4 factorial, next term is zero is the last digit...

I started with adding up the factorials, and I noticed that any factorial after $5!$ will end in 0, because they all contain at least one 5 multiplied with at least one 2. So the last digit would remain unchanged after adding $1!+2!+3!+4!$

Since $1!+2!+3!+4!=1+2+6+24=33$ , the last digit will be three.