I have a little problem with the following exercise.
I have to prove by mathematical induction that for all n real numbers, which’s product is 1, their sum is greater than or equal to n.
I’d be very happy if someone could help me with this.
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If the product of the numbers is , then their GM is . Hence their their sum .
The proof by Induction of this inequality can be found here: Inequality of arithmetic and geometric means - Wikipedia, the free encyclopedia