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How do your use triangular numbers to make square numbers? - Answers

The sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxx



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How do your use triangular numbers to make square numbers? - Answers

https://math.answers.com/basic-math/How_do_your_use_triangular_numbers_to_make_square_numbers

The sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxx



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https://math.answers.com/basic-math/How_do_your_use_triangular_numbers_to_make_square_numbers

How do your use triangular numbers to make square numbers? - Answers

The sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxx

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      The sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxxThe sum of any two successive triangular number is a square number.The nth triangular number is n(n+1)/2 = (n2 +n)/2The next triangular number is (n+1)*(n+2)/2 = (n2 + 3n + 2)/2Their sum is (2n2 + 4n + 2)/2 = n2 + 2n + 1 = (n + 1)2This is easy to visualise. For example T3 + t4 = 42[T3, the 3th triangular number represented by X,t4, the 4th triangular number represented by x]XXX_____xXX_____xxX_____xxx_____xxxxBring them together and you have:XXXxXXxxXxxxxxxx
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