14. Sequences & Series
Review of Factorials
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Evaluate the expression.
A
2!
B
63
C
72
D
98
Verified step by step guidance1
Step 1: Understand the factorial notation. The factorial of a number n, denoted as n!, is the product of all positive integers from 1 to n. For example, 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1.
Step 2: Simplify the numerator of the given expression, which is 9!. Since the denominator includes 7!, you can cancel out the common terms in the numerator and denominator. This simplifies 9! / 7! to (9 × 8).
Step 3: Multiply the simplified numerator (9 × 8) by 7!. This results in (9 × 8 × 7!).
Step 4: Divide the result from Step 3 by the denominator, which is 2!. Recall that 2! = 2 × 1 = 2. So, divide (9 × 8 × 7!) by 2.
Step 5: Simplify the final expression by performing the division and multiplication. This will yield the final result.
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