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Thread: Arithmetic Mean

  1. #1
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    Arithmetic Mean

    If a < b, show that a < (a + b)/2 < b. The number (a + b)/2 is called the ARITHMETIC MEAN of a and b.
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  2. #2
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    Quote Originally Posted by symmetry View Post
    If a < b, show that a < (a + b)/2 < b. The number (a + b)/2 is called the ARITHMETIC MEAN of a and b.
    Since $\displaystyle a<b$

    Then: $\displaystyle 2a<a+b$

    So: $\displaystyle a<\frac{a+b}{2}$

    Also since $\displaystyle a<b$

    Then: $\displaystyle a+b<2b$

    So: $\displaystyle \frac{a+b}{2}<b$

    Therefore: $\displaystyle a<\frac{a+b}{2}<b$
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    ok

    Very interesting notes in this prove question and answer.
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