Talk:Square pyramidal number: Difference between revisions

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:I'm not sure I see the point of long algebraic derivations at all, given that it's so straightforward to prove any such formula by induction. If you could replace this with a short conceptual visual (and sourced!) proof, that would be better, I think. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 04:06, 7 September 2017 (UTC)
::The proof by induction is indeed not that hard, but you need to know the formula in the first place. This way you get the formula automatically, and the proof isn't long at all (it can be done with one picture, http://forumbgz.ru/user/upload/file580638.jpg (with some unimportant text in russian)). But I'm not sure if some random picture on the internet is considered a source. [[User:MYXOMOPbI4|MYXOMOPbI4]] ([[User talk:MYXOMOPbI4|talk]]) 22:53, 7 September 2017 (UTC)
:::It's more or less obvious that the formula is a cubic polynomial and from that and the first four values you can immediately derive it by finite differences. And no, random pictures on the internet, especially from a site whose address syntax suggests that it's an open wiki, are not reliable sources. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 00:27, 8 September 2017 (UTC)