Math Problem Statement

n/n-2!

Solution

The expression you've written, nn2!\frac{n}{n-2!}, contains a factorial. Let's break it down:

  1. Factorial: The factorial of a number xx, denoted x!x!, is the product of all positive integers up to xx. For example:

    • 2!=2×1=22! = 2 \times 1 = 2
  2. Expression: You are dividing nn by n2!n - 2!, which simplifies to: nn2!=nn2\frac{n}{n - 2!} = \frac{n}{n - 2}

This means the expression simplifies to nn2\frac{n}{n - 2}, where the factorial 2!=22! = 2.

Let me know if you'd like more details, or if this clears things up! Here are five related questions for further exploration:

  1. What is the result of nnk!\frac{n}{n - k!} for different values of kk?
  2. How do you compute larger factorials, such as 5!5! or 7!7!?
  3. What happens if n=2n = 2 in your original expression?
  4. How can you apply factorials in probability problems?
  5. How does the factorial function behave as nn approaches infinity?

Tip: When using factorials, always ensure that the input is a non-negative integer, as the factorial function is only defined for such numbers.

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Math Problem Analysis

Mathematical Concepts

Algebra
Factorials
Rational Expressions

Formulas

Factorial: n! = n × (n-1) × ... × 1
Rational Expression: \( \frac{n}{n - k} \)

Theorems

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Suitable Grade Level

Grades 8-10