Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

9. Sequences, Series, & Induction

Sequences

College Algebra

9. Sequences, Series, & Induction

Sequences

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1:04 minutes

Problem 83

Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/300

Verified step by step guidance

Identify the expression to evaluate: \( \frac{20!}{300} \).

Understand that \( 20! \) (20 factorial) means multiplying all whole numbers from 20 down to 1.

Use a calculator with a factorial function to compute \( 20! \).

Divide the result of \( 20! \) by 300 to simplify the expression.

Ensure the calculator is set to handle large numbers, as factorials grow rapidly.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Factorial

The factorial of a non-negative integer n, denoted as n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow very quickly with increasing n, making them useful in permutations, combinations, and other areas of mathematics.

Calculator Functions

Most scientific calculators have a factorial function that allows users to compute factorials easily. This function typically requires the user to input the integer value and then press the factorial key, which is often represented by an exclamation mark (!). Understanding how to use this function is essential for efficiently solving problems involving large factorials.

Division of Factorials

When dividing factorials, such as 20!/300, it is important to simplify the expression where possible. Since 20! is a very large number, direct computation may not be feasible without a calculator. Understanding how to manipulate factorials and perform division helps in evaluating such expressions accurately.