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Unformatted text preview: 4. Let ( x i ,y i ), i = 1 , 2 , 3 , 4 , 5 be a set of ve distinct points with integer coordinates in the xy plane. Show that the midpoint of the line joining at least one pair of these points has integer coordinates. 5. For n Z + , consider the following sum n X i =1 1 (2 i-1)(2 i + 1) . make a conjecture about the formula for the exact value of this sum, and prove your conjecture....
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- Spring '08