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Is the following statement true or false? For every odd integer n , | ~ n 2 ~ | = n + 1 2 To
Is the following statement true or false?
For every odd integer ~~
To answer this question, let be any odd integer. By definition of odd, for some integer and so by substitution, ~~~~ starting with this equality, express ~~ in temes of as simply as possible without using the celling notation. The result is
~~~
Also, when is expressed in terms of and is completely simplified, the result is
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