perplexus.info :: Numbers : Another Square Sequence

Another Square Sequence (Posted on 2003-12-23)

If you subtract the sum of the first x numbers, squared, from the sum of the next x numbers, squared, (for example, 6² + 5² + 4² - 3² - 2² - 1²); you will get (x²)(2x+1) and also x²(x+1)² minus x^4. Prove why this works.

Submitted by Gamer

Rating: 2.3333 (3 votes)

Solution: (Hide)

A proof by induction was supplied here and a simpler proof based on sum of squares was provided here

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-02-17 05:47:17
re: Proof by Induction	sumit	2004-06-14 08:23:15
solution	sumit	2004-06-14 08:20:05
another solution	luminita	2003-12-28 14:56:43
Proof by Induction	Larry Settle	2003-12-27 13:53:11
No Subject	zaphod	2003-12-24 01:51:43

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