a and b being two strictly positive numbers , compare (a+b)/2 and √a√b
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Originally Posted by lebanon a and b being two strictly positive numbers , compare (a+b)/2 and √a√b Consider .
Then divide by 2 to get . But since is nonnegative for any positive and (why?) it follows that .
Therefore, for any positive numbers and .
And it can further be proven by simple induction that: for and .
Last edited by TheCoffeeMachine; Jan 7th 2011 at 12:24 AM.
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