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.

See The Solution Submitted by Gamer

Rating: 2.3333 (3 votes)

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Puzzle Thoughts

Comment 6 of 6 |

We observe that:

(x^2)(2x+1) = {x^2}{(x^2+2x+1-x^2}

= {x^2}{(x+1)^2-x^2}

=(x^2){(x+1)^2}-x^4

Posted by K Sengupta on 2023-02-17 05:47:17

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