Sum of Cubes (Posted on 2004-05-25)

	Submitted by Gamer
Rating: 3.4000 (5 votes)
Solution:	(Hide)
The sum of perfect cubes up to x³ appears to be equal to ((x+1)(x/2))², so this will be called S(x). One easy way to prove is using induction. Proving S(1) is true: ((1+1)(1/2))² = 1² = 1. Proving S(x)+(x+1)³=S(x+1) is true: ((x+1)(x/2))²+(x+1)³= ((x+1)²/4)(x²)+((x+1)²/4)(4(x+1))= ((x+1)²/4)(x²+4x+4)= ((x+1)²/2²))((x+2)²= (((x+1)+1)(x+1)/2)²

	Subject	Author	Date
	Puzzle Solution: Formal Method	K Sengupta	2022-01-06 01:49:28
	What Gamer perhaps had in mind.	broll	2011-10-10 02:38:30
	Puzzle Solution	K Sengupta	2008-11-27 13:24:04
	Solution	Praneeth	2007-08-14 00:55:25
	re(2): an arbitrary n solution...	ryan	2005-09-20 04:43:38
	re: an arbitrary n solution...	Dan	2005-09-06 08:14:32
	an arbitrary n solution...	ryan	2005-08-14 21:55:39
	solution	Pemmadu Raghu Ramaiah	2005-01-09 02:45:14
	No Subject	Pemmadu Raghu Ramaiah	2005-01-09 02:31:13
	algebraic solution	Danny	2004-05-25 16:45:17
	Difference Method	Richard	2004-05-25 16:06:56
	Solution	e.g.	2004-05-25 13:10:38