Math Problem Statement

6! + 7!

Solution

Let's break it down:

  • 6!=6×5×4×3×2×1=7206! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720
  • 7!=7×6×5×4×3×2×1=50407! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040

Now, we add the two:

6!+7!=720+5040=57606! + 7! = 720 + 5040 = 5760

So, 6!+7!=57606! + 7! = 5760.

Would you like more details on factorials or have any questions?


Here are five related questions for further exploration:

  1. What is 5!+6!5! + 6!?
  2. How does factorial grow as the numbers increase?
  3. What is the sum of 8!+9!8! + 9!?
  4. Can you express n!n! in terms of (n1)!(n-1)!?
  5. What is the factorial of zero, and why is 0!=10! = 1?

Tip: Factorials grow very quickly as nn increases, which is why even small changes in nn can lead to huge differences in the value.

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Math Problem Analysis

Mathematical Concepts

Factorials
Arithmetic Operations

Formulas

n! = n × (n-1) × ... × 1

Theorems

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Suitable Grade Level

Grades 9-10