September 19th, 2018, 12:24 PM |
#1 |

Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,302 Thanks: 935 | Hmmm...
n^4 - n^3 + n^2 - n = n*{n*[n*(n - 1) + 1] - 1} Just got that...kinda accidentally...mean anything? |

September 19th, 2018, 01:06 PM |
#2 |

Newbie Joined: Jul 2018 From: Georgia Posts: 24 Thanks: 5 | |

September 19th, 2018, 02:43 PM |
#3 |

Newbie Joined: Jul 2018 From: Georgia Posts: 24 Thanks: 5 |
Okay, I was being mildly facetious in my first reply. I would like to know how you happened upon that. If you expand from the inside out, starting with what's inside the square brackets, you have: n^2 - n + 1 Next step out - the curly brackets: n^3 - n^2 + n - n And that's the key step. You've got the +n and -n, which are already zero if you're going to do anything else to that entire string. So the key to this seems to be including +1 inside the square brackets, but external to the parentheses, and then including -1 inside the curly brackets but external to the square brackets. Since you're essentially multiplying each 'group'' successively by n, then you've guaranteed producing a +n and a -n by that setup. Was there something else there that you saw or wondered about? |

September 19th, 2018, 02:52 PM |
#4 |

Math Team Joined: May 2013 From: The Astral plane Posts: 1,889 Thanks: 769 Math Focus: Wibbly wobbly timey-wimey stuff. | |

September 19th, 2018, 03:28 PM |
#5 |

Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,302 Thanks: 935 | |

September 19th, 2018, 04:15 PM |
#6 |

Senior Member Joined: Sep 2016 From: USA Posts: 473 Thanks: 262 Math Focus: Dynamical systems, analytic function theory, numerics |
I'm not sure if this is just satirizing the other thread but this formula is actually quite useful. The RHS is how you would evaluate the polynomial, $n^4 - n^3 + n^2 - n$ using Horner's algorithm. If you haven't seen it before its pretty simple but very powerful. https://en.wikipedia.org/wiki/Horner%27s_method |

September 19th, 2018, 06:28 PM |
#7 |

Global Moderator Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond |
I knew that had a name - couldn't think of it though. |