# 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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