\(\pi\)ece of cake

Calculus Level 3

\[ \large \displaystyle\int _{ 1 }^{ \infty }{ \dfrac { dx }{ \lfloor x \rfloor ^{ 2 } } } =\dfrac { { \pi }^{ a } }{ b } \]

The equation above holds true for positive integers \(a\) and \(b\). Find \(a+b\).

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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