Question 318340
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Let *[tex \Large x] represent the first of four consecutive integers.  Then the other three are:  *[tex \Large x\ +\ 1], *[tex \Large x\ +\ 2], and *[tex \Large x\ +\ 3]


Three times the greatest is:  *[tex \Large 3(x\ +\ 3)]


The sum of the other three:  *[tex \Large x\ +\ x\ +\ 1\ +\ x\ +\ 2]


So:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ x\ +\ 1\ +\ x\ +\ 2\ +\ 6\ =\ 3(x\ +\ 3)]


Simplified:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x\ +\ 9\ =\ 3x\ +\ 9]


From which we can see that the stated relationship is valid for ALL integers.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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