Resistor Pyramid

Jo has 8 identical resistors with resistance \(r\). He decides to build a Resistor Pyramid for his Physics project. Being a curious boy, he tries to find out the equivalent resistance between \(A\) and \(B\) using his ohmmeter. Find the equivalent resistance that the ohmmeter shows up when \(r = 1 \Omega \).

If the resistance can be expressed in the form of \(\dfrac{\alpha}{\beta}\), where \(\alpha\) and \(\beta\) care coprime positive integers, submit your answer as \( \alpha + \beta\).

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