Question
What does the following expression mean? \( 7! \) \( 7+6+5+4+3+2+1 \) \( 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 \)
Ask by Davies Schultz. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(7!\) means the product of all numbers from 1 to 7, which is 5040. The sum \(7 + 6 + 5 + 4 + 3 + 2 + 1\) equals 28.
Solution
\(7!\) is read as “7 factorial.” It represents the product of all positive integers from 1 up to 7. In other words:
- \( 7! = 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 \)
On the other hand, the expression
- \( 7+6+5+4+3+2+1 \)
is the sum of the integers from 1 to 7.
So, while both expressions involve the numbers 1 through 7, one calculates their product (which is factorial) and the other calculates their sum. The factorial value \(7!\) is:
\[
7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040
\]
The sum is:
\[
7 + 6 + 5 + 4 + 3 + 2 + 1 = 28
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
The expression \( 7! \) stands for "7 factorial," which is the product of all positive integers from 7 down to 1. So, it’s like a party where everyone from 7 down to 1 gathers to hold hands and count down to the fun! In this case, \( 7! = 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 = 5040 \). Interestingly, \( 7 + 6 + 5 + 4 + 3 + 2 + 1 \) is the sum of those same numbers, which equals 28. This is a classic arithmetic series where you can simply add numbers together, and it's a great mental math exercise! By breaking it down, you can spot patterns: you can pair the highest and lowest numbers like \( (7 + 1), (6 + 2), (5 + 3) \) to make calculations even easier!
