Find the remainder when `sum_(r=1)^(n)r!` is divided by `15`, if `n ge5`.

Explanation

To find the remainder when the sum \( S = \sum_{r=1}^{n} r! \) is divided by 15 for \( n \geq 5 \), we can follow these steps:

### Step 1: Calculate the factorials from 1 to 4
First, we calculate the factorials for \( r = 1, 2, 3, 4 \):
- \( 1! = 1 \)
- \( 2! = 2 \)
- \( 3! = 6 \)
- \( 4! = 24 \)
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