Exponents in Fractions

Algebra Level 4

\[ \large \left( 1 - \dfrac1{2^2} \right)\left( 1 - \dfrac1{3^2} \right)\left( 1 - \dfrac1{4^2} \right)\cdots \left( 1 - \dfrac1{2014^2} \right) \]

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

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