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Math 491, Problem Set \#2 \\
(due 9/16/03)
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\begin{enumerate}
\item
Find necessary and sufficient conditions
for the infinite product $f_1 f_2 f_3 \cdots$ to converge
in the ring of formal power series.
Be sure to take proper care of degenerate cases,
e.g., where one of the $f_n$'s actually is 0.
A detailed proof is not required.
\item
By comparing the expansions of
$1/(1-x-x^2)$ and $1/(1-x-y)$,
derive a formula for the Fibonacci numbers
as sums of binomial coefficients.
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\noindent
Please be sure to write down how many hours you spent working on
each of the two problems in the assignment,
and to write down whom you worked with.
You should do this for ALL your assignments for this course.
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