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Chapter 8: Problem 78

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

Short Answer

Expert verified
By using the property of factorials, \(\frac{900 !}{899 !}\) simplifies to 900.

Step by step solution

01

Understand Factorial Notation

Factorial notation often presented as (n!). It means the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
02

Applying Factorial Property

The next step is to use the property of factorials where the factorial of a number n (n!) is equal to n times the factorial of (n-1). As so, \( n! = n 脳 (n-1)! \). Whenever this rule applies, you can simplify the expression.
03

Simplify The Expression

Applying the factorial property, 900! can also be written as (900 x 899!) So, the expression becomes \(\frac{900 x 899 !}{899 !}\). As you can see, 899! is common in the numerator and the denominator. So, it cancels out.
04

Final Calculation

After the 899! cancels out, the final expression becomes 900. Hence, \(\frac{900 !}{899 !}\) = 900 without any computation.

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