# Fibonacci is Golden

Algebra Level 4

$\large \lim_{n\to\infty}\sum_{k=1}^{2n} \left [ (-1)^k\frac{F_k}{\phi^k} \right ]$ Find the limit above, where $$F_k$$ is the $$k$$-th Fibonacci number, $$\phi$$ is the Golden Ratio, and $$n$$ is a positive integer.

Answers in decimal form are accepted. If you find that the limit fails to exist, enter 0.666 as your answer.

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