Happy new 2015 Year !!!!

Calculus Level 5

What is the infimum(minimum) value of \[\sqrt { \frac { { a }_{ 1 } }{ { a }_{ 2 }+{ a }_{ 3\quad }+\ldots +{ a }_{ 2015 } } } +\sqrt { \frac { { a }_{ 2 } }{ { a }_{ 1 }+{ a }_{ 3 }+\ldots +{ a }_{ 2015 } } } +\ldots + \\ \sqrt { \frac { { a }_{ 2014 } }{ { a }_{ 1 }+{ a }_{ 2 }+\ldots +{ a }_{ 2013 }+{ a }_{ 2015 } } } +\sqrt { \frac { { a }_{ 2015 } }{ { a }_{ 1 }+{ a }_{ 2 }+\ldots+{ a }_{ 2013 }+{ a }_{ 2014 } } } ? \]

Details and assumptions:
- \({ a }_{ 1 }, { a }_{ 2 }, ... , { a }_{ 2014 }, { a }_{ 2015 } \) are positive real numbers!
- Enter your answer to two decimals!
- This problem was inspired by "2015 is coming!!!!" by Martin Nikolov!

×

Problem Loading...

Note Loading...

Set Loading...