roles) || in_array('administrator', $user->roles) || in_array('admin', $user->roles ) ) { ?>
probname); ?>
Topic Classification: nid, "Topic Classification"); ?> Tags: nid, "Problem Tag");?>
Topics: nid, "Topics"); ?> Prerequisites: nid, "Prerequisites"); ?>
Supplies: nid, "Supplies"); ?> Pedagogy: nid, "Pedagogy"); ?>
Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
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Solution: nid, "Solution"); ?>
Problem

We will prove the statement $P(n): x_1 x_2 \ldots x_n \leq \left( {\displaystyle\frac{x_1 + x_2 + \cdots + x_n}{n}} \right) ^n$
for all positive $x_i$.
a)By setting $x_n = \displaystyle\frac{x_1 + x_2 + \cdots + x_{n-1}}{n-1}$, prove that $P(n)$ implies $P(n-1)$ for all $n > 1$.
b)Show that $P(n)$ and $P(2)$ imply $P(2n)$.
c)Explain why this proves $P(n)$ is true for all $n$.

Details
Contributer: Josh
Authors
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References
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Reference Author Reference Title Reference URL
'; } ?>
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Problem Sets This Problem Belongs to:
parent_nid; ?> Set:
VARIABLES
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DEFINITIONS
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