Find one interesting pattern in Square numbers
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1, 4, 9, 16, 25, 36, 49… And now find the difference between consecutive squares: 1 to 4 = 3 4 to 9 = 5 9 to 16 = 7 16 to 25 = 9 25 to 36 = 11 …
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An Algebraist's Epiphany
We have two consecutive numbers, n and (n+1)
Their squares are n2 and (n+1) ...
The difference is (n+1)2 – n2 = (n2+ 2n + 1) – n2 = 2n + 1.
Step-by-step explanation:
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