Question: (1)Prove that the difference of two consecutive triangular numbers represented by n ( n + 1 ) / 2 is a perfect cube.Be careful with

(1)Prove that the difference of two consecutive triangular numbers represented byn(n+1)/2 is a perfect cube.Be careful with the indexing.

(2)Prove that the difference of two rational numbers is a rational number.(use details)

(3)Prove, by contradiction, that the product of a rational and an irrational number is irrational.

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