# Peculiar Sums

Calculus Level 3

$\displaystyle A = \sum_{n=1}^\infty \left ( \dfrac{1}{\phi}\right )^{n} , \qquad B= \displaystyle \sum_{n=0}^\infty \left( \dfrac{1}{\phi^{2}} \right)^{n}$

Let $$\phi$$ denote the golden ratio, $$\phi = \frac{1+\sqrt5}2$$. Then find the value of $$A+B$$.

Give your answer to 3 decimal places.


Hint: $$\frac 1\phi = \phi - 1$$.

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