If a_1, a_2, dots, a_n are positive real numb | vedclass

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(C) For positive real numbers $a_1, a_2, \dots, a_n$,the Arithmetic Mean-Geometric Mean $(AM-GM)$ inequality states that $AM \ge GM$.$	herefore \frac

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Not less than $n$.

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(C) For positive real numbers $a_1, a_2, \dots, a_n$,the Arithmetic Mean-Geometric Mean $(AM-GM)$ inequality states that $AM \ge GM$.$	herefore \frac{a_1 + a_2 + \dots + a_n}{n} \ge (a_1 \cdot a_2 \cdot \dots \cdot a_n)^{\frac{1}{n}}$Given $a_1 \cdot a_2 \cdot \dots \cdot a_n = 1$,we substitute this into the inequality:$	herefore \frac{a_1 + a_2 + \dots + a_n}{n} \ge (1)^{\frac{1}{n}}$$	herefore \frac{a_1 + a_2 + \dots + a_n}{n} \ge 1$$	herefore a_1 + a_2 + \dots + a_n \ge n$Thus,the sum of the numbers is not less than $n$.

If $a_1, a_2, \dots, a_n$ are positive real numbers such that $a_1 \cdot a_2 \cdot \dots \cdot a_n = 1$,then their sum is:

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