# 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.

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