Problem 9 In your own words, explain how t... [FREE SOLUTION]

Chapter 15: Problem 9

In your own words, explain how to evaluate \(n !\) for any positive integer.

Short Answer

Expert verified

To evaluate the factorial of a positive integer \(n\), denoted as \(n!\), follow these steps: 1. Understand that the factorial function is the product of all positive integers up to the given number: \[n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1\] 2. Identify the given positive integer (n) for which you need to find the factorial. 3. Multiply the given integer by all the positive integers smaller than it in descending order: \[n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1\] 4. Simplify the product to get the resulting value of \(n!\).

Step by step solution

Understand the concept of Factorial

Factorial is a mathematical function denoted by an exclamation mark (\(!\)), and it represents the product of all positive integers up to a given number (n). The factorial function is defined as: \[n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1\] For example, the factorial of \(5\) is: \[5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\] Please note that the factorial of \(0\) is defined as \(1\), i.e., \(0! = 1\).

Identify the given positive integer

To evaluate the factorial of a positive integer, first, identify the number you are given (n). Make sure it is a positive integer before proceeding with the computation as factorials are defined only for non-negative integers.

Multiply the integer by all its preceding positive integers

Now, you can start computing \(n!\) by multiplying the given positive integer with all positive integers smaller than it in descending order: \[n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1\] For example, if we want to find the factorial of \(4\): \[4! = 4 \times 3 \times 2 \times 1 = 24\]

Simplify and write the result

Once you have calculated the product, simplify and write it down as the result. In the example of \(4!\), the result is 24. So, to evaluate \(n!\) for any positive integer, follow these steps: 1. Understand the concept of factorial. 2. Identify the given positive integer (n). 3. Multiply the integer by all its preceding positive integers. 4. Simplify and write the result.

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91影视

In your own words, explain how to evaluate \(n !\) for any positive integer.

Short Answer

Step by step solution

Understand the concept of Factorial

Identify the given positive integer

Multiply the integer by all its preceding positive integers

Simplify and write the result

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