Sums of Consecutive Odd vs. Even Integers
Date: 04/15/2002 at 18:51:42 From: Charles Subject: Math Portfolio Can the sum of two consecutive even integers ever equal the sum of two consecutive odd integers? Why or Why not?
Date: 04/15/2002 at 23:29:45 From: Doctor Ian Subject: Re: Math Portfolio Hi Charles, Any odd integer can be written as 2*k + 1 where k is some integer. Try some examples, to convince yourself that it's true. (For example, 7 is odd; and it can be written as 2*3 + 1.) That means that we can write any two consecutive odd integers as 2*k + 1 and 2*k + 3 If we add these together, we get 2*k + 1 + 2*k + 3 = 4*k + 4 Following the same kind of reasoning, what happens if you add two consecutive even integers together? Can you ever get something that looks like 4*k + 4? I hope this helps. Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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