.

Simplify the infinite convergent sum as much as possible in terms of $\displaystyle \phi$:

$\displaystyle \dfrac{1}{\phi^1} + \dfrac{1}{\phi^2} + \dfrac{1}{\phi^3} \ + \ ... $

where $\displaystyle \phi$ equals $\displaystyle \dfrac{\sqrt{5} + 1}{2}$.

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Source:

The Call Of The Primes: Surprising Patterns, Peculiar Puzzles, and Other Marvels of Mathematics

by Owen O'Shea

pages 123, 125-126