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

Algebra Level 4

Which of the following is the largest?

A. 211211211211...\sqrt{2^{11}\sqrt{2^{11}\sqrt{2^{11}\sqrt{2^{11}\sqrt{...}}}}}-33333333...\sqrt{33\sqrt{33\sqrt{33\sqrt{33\sqrt{...}}}}}

B. 12+11+20142014+11+20132013+11+20122012+...\frac{1}{2}+\frac{1}{1+2014^{-2014}}+\frac{1}{1+2013^{-2013}}+\frac{1}{1+2012^{-2012}}+... +11+20122012+11+20132013+11+20142014+\frac{1}{1+2012^{2012}}+\frac{1}{1+2013^{2013}}+\frac{1}{1+2014^{2014}}

C. 1008×(1122)1×(1132)1×(1142)1...1008\times(1-\frac{1}{2^{2}})^{-1}\times(1-\frac{1}{3^{2}})^{-1}\times(1-\frac{1}{4^{2}})^{-1}... (1120132)1×(1120142)1×(1120152)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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