Problem 60 - Algebra and Trigonometry

Question

Will help you prepare for the material covered in the first section of the next chapter. Find the product of all positive integers from \(n\) down through 1 for \(n=5\)

Step-by-Step Solution

Answer

The product of all positive integers from 5 down through 1 (also known as \(5!\)) is 120.

Step 1: Understand the definition of a factorial

The factorial of a number \(n\) (usually represented as \(n!\)) is the product of all positive integers from \(n\) through 1. Thus, the task here is to find \(5!\).

Step 2: Compute the factorial of 5

Calculate \(5!\) by multiplying together all positive integers from 5 down through 1: \(5! = 5 \times 4 \times 3 \times 2 \times 1\)

Step 3: Perform the multiplication

Perform the multiplication: \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\)