Hi All,

I wanted to understand the logic behind why arithmetic mean is greater than geometric mean, can someone please explain me

Hi All,

I wanted to understand the logic behind why arithmetic mean is greater than geometric mean, can someone please explain me

Here’s a proof when you have two values; I’ll leave the proof for more than two values to you.

\left(\sqrt{a} - \sqrt{b}\right)^2 \geq 0

\left(\sqrt{a}\right)^2 - 2\sqrt{a}\sqrt{b} + \left(\sqrt{b}\right)^2 = a - 2\sqrt{ab} + b \geq 0

a + b \geq 2\sqrt{ab}

\frac{a + b}{2} \geq \sqrt{ab}

QED

I also Googled “arithmetic mean vs. geometric mean”. I found all sorts of lovely proofs using logarithms, induction, etc.