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Chapter 10: Problem 78

Explain the best way to evaluate \(\frac{900 !}{899 !}\) without a calculator.

Short Answer

Expert verified
Therefore, \(\frac{900!}{899!} = 900\)

Step by step solution

01

Explanation and Definition

The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Notably, it should be understood that \(n!=n*(n-1)!\). This property will be used in the subsequent step to simplify the fraction.
02

Application of Factorial Properties

Apply the above property to the fraction. You can substitute 900! with \(900*899!\) in the numerator, which results in \(\frac{900*899!}{899!}\).
03

Cancellation

Now, you observe that \(899!\) is a common factor in both the numerator and the denominator of the fraction. Was, they cancel out, leaving only 900 as the solution.

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