Calculate the digit in the unit's place of the number 2! + 3! +...........99! .
The key to this problem is realizing that factorials past 5! have a units digit of 0. (Make sure you see why)
Therefore, we only have to look at 2! + 3! + 4! = 2 + 6 + 24 = 32
So the units digit is 2.