Waste less time on Facebook — follow Brilliant.
×

NMTC 2nd Level 2014

Let \({ a }_{ 1 }{ a }_{ 2 }{ ...a }_{ 2014 }\) be a random arrangement of \(1,2,3...2014\). Prove that

\(\frac { 1 }{ { a }_{ 1 }{ +a }_{ 2 } } +\frac { 1 }{ { a }_{ 2 }+{ a }_{ 3 } } +.....\frac { 1 }{ { a }_{ 2012 }{ +a }_{ 2013 } } +\frac { 1 }{ { a }_{ 2013 }{ +a }_{ 2014 } } >\frac { 2013 }{ 2016 } \)

This a part of my set NMTC 2nd Level (Junior) held in 2014.

Note by Siddharth G
2 years, 11 months ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Hint: Apply Titu-lemma(Cauchy inequality) , and then use \( a_1+a_{2014} \ge 3 \)

Shivang Jindal - 2 years, 11 months ago

Log in to reply

Thanks! I also found an AM-HM solution along the way.

Siddharth G - 2 years, 11 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...