Math Problem Statement
- Let a1, a2, ..., an be positive real numbers. Prove by mathematical indution that the arithmetic mean of these numbers is greater or equals to the geometric mean.
Solution
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Math Problem Analysis
Mathematical Concepts
Arithmetic Mean
Geometric Mean
Mathematical Induction
Inequality
Formulas
Arithmetic Mean: (a1 + a2 + ... + an) / n
Geometric Mean: (a1 * a2 * ... * an)^(1/n)
AM-GM Inequality: (a1 + a2 + ... + an) / n >= (a1 * a2 * ... * an)^(1/n)
Theorems
AM-GM Inequality
Principle of Mathematical Induction
Suitable Grade Level
Grades 11-12 or College Level
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