# 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

Note by Department 8
2 years, 4 months ago

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

Staff - 2 years, 4 months ago