step 1 Okay, so n times what gives us n factorial? Well, that means we need all of our previous terms b

Question

$$n \cdot \quad=n !$$

Name: Problem 7, Chapter 8: College Algebra
Uploaded: 2020-07-06T21:28:27-08:00
Duration: 21 s
Channel: Amy Jiang
Description: n · =n !

   $$n \cdot \quad=n !$$

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 7

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

Step 1

Step 1: We are given the equation $n \cdot \quad=n !$, and we need to find what should be filled in the blank to make the equation true. Show more…

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$$n \cdot \quad=n !$$

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Key Concepts

Factorial Function

The factorial function is a mathematical operation that multiplies a positive integer by all the smaller positive integers. It is denoted as n! and defined as n! = n × (n - 1) × (n - 2) × ... × 1, with the special case 0! = 1. This operation is fundamental in combinatorics, probability, and various areas of mathematics where ordering and arrangements are considered.

Recursive Definition of Factorial

The factorial function can be understood recursively, meaning that each value is defined in terms of previous values. Specifically, n! = n × (n - 1)! for any integer n > 0, with 0! defined as 1. This recursive relationship not only provides a concise way to describe the factorial function but also simplifies computational algorithms and proofs in mathematical analysis.

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