Power Series
The generating function of the Fibonacci sequence is the power series
This series has a simple and interesting closed-form solution for :
This solution can be proven by using the Fibonacci recurrence to expand each coefficient in the infinite sum defining :
Solving the equation for results in the closed form solution.
In particular, math puzzle-books note the curious value, or more generally
for all integers .
More generally,
Read more about this topic: Fibonacci Numbers
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