In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 200!/198!

Key Concepts

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.

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.

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.