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Correction term

You can add a correction term to the times tables, to get a usable result even when multiplying with zero, so that

S0 = 0 × n + 00 = 1

 


Explanation

With a drawing you can nicely show the table of 8. The first border has 8 balls, the second 16, etc.

0   1   2   3   4   5   6   7   8   9   10

So you see exactly the table of 8, which gives

1 × 8 =  8
2 × 8 = 16
3 × 8 = 24
4 × 8 = 32
5 × 8 = 40
6 × 8 = 48
7 × 8 = 56
8 × 8 = 64
9 × 8 = 72
10 × 8 = 80

The center is empty, because 0 × 8 = 0. If you also want to have a ball there you should work with the formula

Number of balls per border = n × 8 + 0n

Here emerges zero to the zero power, and that gives 0 × 8 + 00 = 0 + 1 = 1.

 


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