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Chapter 14: Problem 64

Explain how to find \(n !\) if \(n\) is a positive integer.

Short Answer

Expert verified
The factorial of a positive number \(n\), denoted \(n!\), is the product of all integers from 1 to \(n\). It is calculated by initializing a result to 1, and then iteratively multiplying this result by each integer from 1 to \(n\). At the end of this process, the result is \(n!\).

Step by step solution

01

Understand Factorial

The factorial of a positive integer \(n\), denoted by \(n!\), is the product of all positive integers less than or equal to \(n\). For example, the factorial of 5 would be represented as \(5! = 5 脳 4 脳 3 脳 2 脳 1\). The factorial function can be defined by the product \(n! = n 脳 (n-1)!\) for \(n > 0\). Additionally, it is defined that \(0! = 1\).
02

Start With Initial Value

Initialize a variable, say \(result\), to 1. This will hold the final calculation of the factorial.
03

Iterative Process

Iterate from 1 to \(n\) (both inclusive). For each iterated value \(i\), multiply it with the variable result.
04

Update Result

With each iteration, update the result variable by setting \(result = result 脳 i\), where \(i\) is the current integer.
05

Final Result

After the loop finishes running, value of \(result\) will be \(n!\), the factorial of the number \(n\).

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