# 2015 Countdown Problem #4: Find the Largest - Part I

**Algebra**Level 4

Which of the following is the largest?

A. \(\sqrt{2^{11}\sqrt{2^{11}\sqrt{2^{11}\sqrt{2^{11}\sqrt{...}}}}}-\)\(\sqrt{33\sqrt{33\sqrt{33\sqrt{33\sqrt{...}}}}}\)

B. \(\frac{1}{2}+\frac{1}{1+2014^{-2014}}+\frac{1}{1+2013^{-2013}}+\frac{1}{1+2012^{-2012}}+...\) \(+\frac{1}{1+2012^{2012}}+\frac{1}{1+2013^{2013}}+\frac{1}{1+2014^{2014}}\)

C. \(1008\times(1-\frac{1}{2^{2}})^{-1}\times(1-\frac{1}{3^{2}})^{-1}\times(1-\frac{1}{4^{2}})^{-1}...\) \((1-\frac{1}{2013^{2}})^{-1}\times(1-\frac{1}{2014^{2}})^{-1}\times(1-\frac{1}{2015^{2}})^{-1}\)

*This problem is part of the set 2015 Countdown Problems.*