A little thought

Calculus Level 5

\[\large \left( \sum_{n=1}^{\infty} \frac{\varphi(n)(1-\phi)^{n}}{F_{n}} \right)^{-2} = \ ? \]

Note:

  • \(\varphi\) is the Euler totient function.
  • \(\phi = \frac{1+\sqrt{5}}{2}\).
  • \(F_{n}\) is the \(n\)-th Fibonacci number.
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