Unequal

\[\large{\frac { { { a }_{ 1 } } }{ { a }_{ 2 }^{ 2 }+1 } +\frac { { a }_{ 2 } }{ { a }_{ 3 }^{ 2 }+1 } +......+\frac { { a }_{ n } }{ { a }_{ 1 }^{ 2 }+1 } }\]

Let $n$ be an integer greater than $3$ , and let $a_1, a_2, \cdots, a_n$ be non-negative real numbers with $a_1+a_2+......+a_n=2$ . Determine the minimum value of expression above.

The question was given by my friend who gave the Girls Math Olympiad. This was the only question we were not able to solve

#Algebra

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
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Comments

Are you familiar with Classical inequalities? Which one would you use?

Calvin Lin Staff - 5 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$