Math Problem Statement

Calculate the result of the expression (91! - 81!) / 71.

Solution

The image shows the following mathematical expression:

91!81!71\frac{91! - 81!}{71}

Where:

  • 91!91! is the factorial of 91,
  • 81!81! is the factorial of 81,
  • The result of the subtraction is then divided by 71.

To solve this:

  1. Compute 91!91! (factorial of 91).
  2. Compute 81!81! (factorial of 81).
  3. Subtract 81!81! from 91!91!.
  4. Divide the result by 71.

Let me calculate this for you.The result of the expression 91!81!71\frac{91! - 81!}{71} is:

1.904×10120(in standard form)1.904 \times 10^{120} \quad \text{(in standard form)}

This is a very large number.

Would you like more details, or do you have any questions?

Here are five related questions:

  1. What is a factorial, and how is it computed?
  2. How does the growth of factorials affect such expressions?
  3. How does the division by a constant like 71 influence the result?
  4. What are some practical applications of factorials in mathematics?
  5. How can you simplify large factorial expressions using approximation methods like Stirling's approximation?

Tip: When dealing with large factorials, using logarithms or approximations can help simplify computations and avoid huge numbers.

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Math Problem Analysis

Mathematical Concepts

Factorials
Subtraction
Division

Formulas

n! = n × (n-1) × ... × 3 × 2 × 1
(a - b) / c

Theorems

-

Suitable Grade Level

College