How to find a formula for the sum of squares 1 + 4 + 9 + ...
+ n^{2} (See also "Young
Gauss"), and the sum of cubes 1 + 8 + 27 + ... + n^{3}?

Squares

x: | 1 | 2 | 3 | 4 |

y: | 1 | 4 | 9 | 16 |

Find a polynomial of 3^{rd} degree.

Cubes

x: | 1 | 2 | 3 | 4 | 5 |

y: | 1 | 8 | 27 | 64 | 125 |

Find a polynomial of 5^{th} 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 2^{nd} degree. (Here you need
to start with n = 2 or more.)

Calculus Index