Show that adding all the numbers that are not crossed off from 1 to the end of a line, the result is a 4^th power.

Example: 1+4+5+6=16=2⁴

1, 1+3*5,1+3*5+5*13,1+3*5+5*13+7*25,...

First part of each term added is (2n-1), second part is (2n(n-1)+1), so the whole thing is: sum 1 to n (2n-1)(2n(n-1)+1) = n^4.

I'm sure there are neater ways of doing it.

Edited on June 28, 2016, 12:44 am

Posted by broll on 2016-06-28 00:39:20