Exponents in Fractions

Algebra Level 4

(1122)(1132)(1142)(1120142) \large \left( 1 - \dfrac1{2^2} \right)\left( 1 - \dfrac1{3^2} \right)\left( 1 - \dfrac1{4^2} \right)\cdots \left( 1 - \dfrac1{2014^2} \right)

If the value of the expression above is in the form of xy \dfrac xy, where xx and yy are coprime positive integers, find the sum of digits of x+yx+y.

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