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
Famous quotes containing the words power and/or series:
“When power becomes gracious and descends into the visiblesuch descent I call beauty.”
—Friedrich Nietzsche (18441900)
“The theory of truth is a series of truisms.”
—J.L. (John Langshaw)