perplexus.info :: Numbers : Pascal revisited

Pascal revisited (Posted on 2018-05-28)

To evaluate the square of any integer in column 2 - just add to its neighbor's value the 3rd integer in a row below it: e.g. 3²=3+6; 10²=45+55

Explain why it works!

No Solution Yet Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

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Algebraic (spoiler)

Comment 1 of 1

Its right-hand neighbor = C(n,2) = n(n-1)/2

The third integer in the row below = C(n+1,2) = n(n+1)/2

Their sum = ((n^2 - n) + (n^2 + n))/2 = n^2

Posted by Steve Herman on 2018-05-28 18:35:52

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