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