Here are the essential concepts you must grasp in order to answer the question correctly.
Factorial Definition
A factorial, denoted as n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are used in various mathematical contexts, including permutations and combinations, and they grow very quickly as n increases.
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Simplifying Factorials
When evaluating expressions involving factorials, simplification can often be applied. For instance, 200!/198! can be simplified by recognizing that 200! = 200 × 199 × 198!. This allows for cancellation of the 198! in the numerator and denominator, making calculations more manageable.
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Calculator Functions
Most scientific calculators have a factorial function, typically labeled as 'n!'. This function allows users to compute factorials directly without manually multiplying the integers. Understanding how to use this function is essential for efficiently solving problems involving large factorials.
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