Can you show that (x1 + x2 + ... + xn)^n <= (x1*x2*...*xn) by a multinomial argument?
I am attempting to prove that the geometric mean of two numbers is always less than or equal to the arithmetic mean of those two numbers. I want to use the MVT to do this proof, but where do I start?
I know to use the square root function, but what interval do I need to use the MVT on? How do I do this proof?