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The Golden ratio! 2

Algebra Level 3

If \( \phi = \dfrac{1+\sqrt5}2 \), compute \( \dfrac1\phi + \dfrac1{\phi^3}+ \dfrac1{\phi^5}+ \dfrac1{\phi^7} + \cdots \).

\[ \frac \phi2\] 1 \[ \phi \] \[ \phi ^2 \]

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by Abdelghani ßoris

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