How to find a formula for the sum of squares 1 + 4 + 9 + ... + n2 (See also "Young Gauss"), and the sum of cubes 1 + 8 + 27 + ... + n3?
Squares
| x: | 1 | 2 | 3 | 4 |
| y: | 1 | 4 | 9 | 16 |
Find a polynomial of 3rd degree.
Cubes
| x: | 1 | 2 | 3 | 4 | 5 |
| y: | 1 | 8 | 27 | 64 | 125 |
Find a polynomial of 5th degree.
How many cubelets are on the surface of an n*n*n cube?
| x: | 2 | 3 | 4 |
| y: | 8 | 26 | 56 |
Find a polynomial of 2nd degree. (Here you need to start with n = 2 or more.)