Let's go up a floor

Algebra Level 4

\[ \large \left\lfloor \sum_{x=1}^\infty \dfrac1{x^2} + \sum_{x=1}^\infty \dfrac1{3^x} \right \rfloor = \sum_{x=2}^\infty \dfrac{n}{x^2} + \sum_{x=2}^\infty \dfrac n{4^x} \]

The equation above has a real solution \(n\), which can be expressed in the form \(n=\frac { C }{ A{ \pi }^{ A }-B } \). If \(A\), \(B\), and \(C\) are positive integers, find \(A+B+C\).

This problem is original.

Picture credits: HK Bank of China Tower by WiNG, Wikipedia


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