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

#### This problem is original.

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

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 \(A+B+C\).

×

Problem Loading...

Note Loading...

Set Loading...