Summary: Project 4: Fibonacci numbers
Due: Friday, December 10
Define the Fibonacci numbers by a0 = 0; a1 = 1; and for n 2,
an = an-2 + an-1. (1)
Thus, the first few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, . . .. The goal of this project is to
find an explicit formula for an.
Define a power series
f (x) =
= x + x2
+ · · · . (2)
1. In the following, always reindex your answer so that it is of the form n?(??)xn.
(a) Write down the power series x f (x).
(b) Write down the power series x2 f (x).
(c) Write down the power series x f (x) + x2 f (x).