What happens when you add up pairs of consecutive triangular numbers? That is, take 1 + 3, 3 + 6, 6 + 10, 10 + 15, … ? Which sequence do you get? Why? Can you explain it with a picture?
What happens when you add up pairs of consecutive triangular numbers? That is, take 1 + 3, 3 + 6, 6 + 10, 10 + 15, … ? Which sequence do you get? Why? Can you explain it with a picture?
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Sequence When Adding Pairs of Consecutive Triangular Numbers:
When I add pairs of consecutive triangular numbers (e.g., 1 + 3 = 4, 3 + 6 = 9, 6 + 10 = 16, …), I get square numbers (4, 9, 16, …). This happens because each pair of triangular numbers combines to form a perfect square and I can represent this pictorially by rearranging the dots of two triangular numbers into a square.
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