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What are the Triangle numbers up to 21?

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What are the first 12 triangle numbers?

1 (1) 3 (1 + 2) 6 (1 + 2 + 3) 10 (1 + 2 + 3 + 4) 15 (1 + 2 + 3 + 4 + 5) 21 (1 + 2 + 3 + 4 + 5 + 6) 28 (1 + 2 + 3 + 4 + 5 + 6 + 7) 36 (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) 45 (1 + 2

When do 3 numbers not form a triangle?

3 numbers can't be the lengths of the sides of a triangle if . . . -- any one of them is less than the difference of the other two -- any one of them is more than the sum
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What is a number which is a square number and triangle number?

36 = 62 = Triangle(8) The triangle number formula: T(n) = (n2+n)/2. Here is T(8) graphically: . 1 = T(1) = 1 .. +2 = T(2) = 3 ... +3 = T(3) = 6 .... +4 = 10 ....