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Chapter 11: Problem 78

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

Short Answer

Expert verified
The evaluation of the expression \(\frac{900 !}{899 !}\) gives the result as \(900\).

Step by step solution

01

Understand factorial operation

For any natural number n, the factorial operation (\(n!\)) gives the product of all positive integers less than or equal to n. That is, \(n! = n脳(n鈭�1)脳鈥γ�3脳2脳1\).
02

Apply the property of factorials

The property of factorials presents that \(n!=n脳(n鈭�1)!\). Thus, according to this property, \(900!=900脳899!\).
03

Simplify the expression

Substitute \(900!\) with \(900脳899!\) in the given expression. Thus, \(\frac{900 !}{899 !}= \frac{900脳899 !}{899 !}\). Since \(899 !\) is common in the numerator and denominator, they can be cancelled out. The final result is then \(900\).

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