I will show you the trick of the wonder of addition and multiplication.

1. The wonder of addition and
multiplication
~ Disclosure of the trick ~

2. I will show you the trick of the wonder of
addition and multiplication.

3. 3
4
5
3 4 5
In this case, I took three positive integers, 3, 4 and 5.
Imagine a rectangular solid of 3×4×5.

4. 3
4
5
3 4 5
In fact, the operation ( choose a number on the left-hand
side, write the product of the numbers that were not
chosen and subtract 1 from the number chosen ) means
slicing the rectangular solid.

5. 3
4
5
3 4 5

6. 3 4 5
3
3×5 (×1) = 15
3
3
5 5
3
1

7. 3 4 5
3
3×5 = 15
3
3
5 5
3
1

8. 3 4 5
3 4
3×5 = 15
3×3 = 9
3
3
4
5
3
1
1
3
3

9. 3 4 5
3 4
3
3×5 = 15
3×3 = 9
3×3 = 9
3
3
3
5
3
1
1
3
3
3
3
1
The sum of the numbers on the right-hand side plus
the product of the numbers on the left-hand side
equals the volume of the first rectangular solid at
anytime.

10. 3 4 5
2 3 4
1 2 3
0
15
9
9
9
6
6
6
＋
( 3×4×5 = ) 60
Thus, when 0 appears on the left-hand side, the sum
of the numbers on the right-hand side equals the
product of the numbers that were chosen at first.

11. In this case, we imagined the three-dimensional
rectangular solid.
If you chose 푛 positive integer at first, imagine
a 푛-dimensional rectangular solid.

12. If you want to prove this wonder by formulas,
the formula
푎1푎2 … 푎푖−1 푎푖 − 1 푎푖+1 … 푎푛
+ 푎1푎2 … 푎푖−1푎푖+1 … 푎푛 = 푎1푎2 … 푎푛
is important.
Thank you for watching!