Discussion
What is the remainder when \(1! + 2! + 3! + ... + 50!\) is divided by 10?
Answer: C
We need to find the unit digit of the sum. Let's look at the unit digits of factorials: \(1! = 1\), \(2! = 2\), \(3! = 6\), \(4! = 24\) (unit digit 4), \(5! = 120\) (unit digit 0). For any \(n \ge 5\), \(n!\) will have a factor of 10, so its unit digit will be 0. 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 3. Therefore, the remainder when divided by 10 is 3.
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