That is, **a + b + … + n = a * b * … * n**

When the Sum of Num3ers Equals their Product [Part 1]

2 + 2 = 2 * 2 = 4

etc.

When the Sum of Num3ers Equals their Product [Part 2]

3 + 3/2 = 3 * 3/2 = 9/2

3 + 3/2 + 9/7 = 3 * 3/2 + 9/7 = 3 * 3/2 * 9/7 = 81/14

3 + 3/2 + 9/7 + 81/67

= 3 * 3/2 + 9/7 + 81/67

= 3 * 3/2 * 9/7 + 81/67

= 3 * 3/2 * 9/7 * 81/67

= 6561/938

3 + 3/2 + 9/7 + 81/67 + 6561/5623

= 3 * 3/2 + 9/7 + 81/67 + 6561/5623

= 3 * 3/2 * 9/7 + 81/67 + 6561/5623

= 3 * 3/2 * 9/7 * 81/67 + 6561/5623

= 3 * 3/2 * 9/7 * 81/67 * 6561/5623

= 43046721/5274374

This is also true with **8 & 7**:

8 + 8/7 = 8 * 8/7 = 64/7 = 9 + 1/7

8 * 8/7 * 64/57 = 8 + 8/7 + 64/57

8 * 8/7 * 64/57 = 4096/399

8 + 8/7 + 64/57 = 4096/399

8 * 8/7 * 64/57 * 4096/3697 = 16777216/1475103

It is also true wit **4 & 3**:

4 + 4/3 = 4 * 4/3 = 16/3 = 5 + 1/3

etc.

We get similar results when combining ** (5 & 4), (6 & 5), (7 & 6), … **

**n + n/(n-1) = n * n/(n-1) = n^2/(n-1), n > 1**

n + n/(n-1) + x = n * n/(n-1) * x

n^2 – n + 1 ≠ 0, x = n^2/(n^2 – n + 1), n – 1 ≠ 0

If **n = 3, x = n^2/(n^2 – n + 1) = 9/7**

If **n = 8, x = n^2/(n^2 – n + 1) = 64/57**

**[To Be Continued]**

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## About benvitalis

math grad - Interest: Number theory