The Golden ratio! 2

Algebra Level 3

If ϕ=1+52 \phi = \dfrac{1+\sqrt5}2 , compute 1ϕ+1ϕ3+1ϕ5+1ϕ7+ \dfrac1\phi + \dfrac1{\phi^3}+ \dfrac1{\phi^5}+ \dfrac1{\phi^7} + \cdots .

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