Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




Not registered yet?

#1 2005-10-18 03:13:45


how to demonstrate this...

This is in the real numbers.

And n>=2, ai>0 (i=1...n).


#2 2005-10-18 14:44:52

Power Member


Re: how to demonstrate this...

I'm not sure if I understand what you're asking, but here goes.

I think here:


You meant to say: (1+a1)(1+a2) that would make a lot more sense.

n >=2, so let's start with the minimum case: n=2.

(1+a1)(1+a2) = 1 + a1 + a2 + a1a2
1+(a1+a2) = 1 + a1 + a2

The first expression > the second, because there's that extra a1a2 term in there.

This will be true for any n >= 2! This is because the expanded multiplication will always have all the terms of the simple addition, plus some additionals that are combinations of the a's.

That proof probably wouldn't satisfy a mathematician, but it sure works for me.

El que pega primero pega dos veces.

Board footer

Powered by FluxBB