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2020 AMC 12B Question 6

AMC12 · 2020 AMC 12B

Question 6

For all integers $n \ge 9,$ the value of

$$
\frac{(n + 2)! - (n + 1)!}{n!}
$$

is always which of the following?
  1. a multiple of $4$
  2. a multiple of $10$
  3. a prime number
  4. a perfect square
  5. a perfect cube