Thread: 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.

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

Then:

So:

Also since

Then:

So:

Therefore:

Very interesting notes in this prove question and answer.