Discussion

The number N = 1! + 2! + 3! + ... + 1000!. What is the unit digit of N?

Answer: C

To find the unit digit of the sum, we observe the unit digits of the individual factorials. \(1!=1\), \(2!=2\), \(3!=6\), \(4!=24\) (unit digit 4). For any factorial \(n!\) where \(n \ge 5\), the unit digit is 0. So all terms from 5! onwards have a unit digit of 0. We only need to sum the unit digits of the first four terms: \(1 + 2 + 6 + 4 = 13\). The unit digit of the sum is 3.