# Arithmetic Mean

• Jan 10th 2007, 01:05 PM
symmetry
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.
• Jan 10th 2007, 01:11 PM
Quick
Quote:

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 $a

Then: $2a

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

Also since $a

Then: $a+b<2b$

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

Therefore: $a<\frac{a+b}{2}
• Jan 10th 2007, 03:50 PM
symmetry
ok
Very interesting notes in this prove question and answer.