Discussion
What is the unit digit of \(1! + 2! + 3! + ... + 50!\)?
Answer: C
To find the unit digit of the sum, we look at the unit digits of the individual factorials. \(1! = 1\), \(2! = 2\), \(3! = 6\), \(4! = 24\) (unit digit 4). For any \(n \ge 5\), \(n!\) will have a unit digit of 0, as it contains factors of 2 and 5. Therefore, we only need to sum the unit digits of the first four factorials: \(1 + 2 + 6 + 4 = 13\). The unit digit of the sum is the unit digit of 13, which is 3.
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