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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Originally Posted by symmetry 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: $\displaystyle a<\frac{a+b}{2}<b$
Very interesting notes in this prove question and answer.
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