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Math Help - 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 a<b

    Then: 2a<a+b

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

    Also since a<b

    Then: a+b<2b

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

    Therefore: a<\frac{a+b}{2}<b
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  3. #3
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    ok

    Very interesting notes in this prove question and answer.
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