Write the first 4 terms of the sequence $a_n=n^2\cdot (n-1)!$

• A. {1, 4, 18, 96}
• B. {1, 2, 6, 24}
• C. {0, 4, 18, 96}
• D. {0, 2, 6, 24}

Answer: (A)

Verified step by step guidance

1. Understand that a factorial, denoted by \(n!\), is the product of all positive integers from 1 up to \(n\). For example, \$5! = 5 \times 4 \times 3 \times 2 \times 1$.
2. Identify the specific factorial expressions or numbers you need to work with in the problem. Since the problem is titled 'Factorials Practice 4', it likely involves simplifying or comparing factorial expressions.
3. If the problem involves simplifying factorial expressions, look for opportunities to cancel common terms. For example, \(\frac{7!}{5!} = \frac{7 \times 6 \times 5!}{5!}\), where \$5!$ cancels out.
4. Rewrite the factorial expressions by expanding only as much as needed to cancel terms, rather than fully expanding the factorials, to keep calculations manageable.
5. After canceling common terms, multiply the remaining numbers to simplify the expression further, if required by the problem.