## Triangle NumbersSeries teasers are where you try to complete the sequence of a series of letters, numbers or objects.Triangle numbers are formed by adding successive integers, i.e.
1 = 1+0, 3 = 1+2, 6 = 1+2+3, 10 = 1+2+3+4, etc. So the first few triangle numbers would be: 1,3,6,10,15,21,28, ... Suppose somebody tells you a random integer. How can you quickly find out whether or not it is a triangle number? ## AnswerMultiply the number by 8 then add 1. If the result is a perfect square, then the original number is a triangle number.For example: 10*8+1 = 81. 81 = 9^2. So 10 is a triangle number. 11*8+1 = 89. 89 is not a perfect square, so 11 is not a triangle number. Hide ## What Next?
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