\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Use the formula
$ {a \over {1 -r }} = a + ar + ar^2 + ar^3 + \cdots$
valid for  $|r| < 1$ to express
each of the following functions as a power series $ a_0 + a_1 x + a_2
x^2 + \cdots + a_n x^n + \cdots$. Give a formula for the coefficient
$a_n$ in each case.
$$
f(x) = { {x}\over {1-x} };\quad 
g(x) = { {2}\over{3x^4 + 16} },
$$

\noindent b) Determine the interval of $x$ values in which each series
in part a) converges (be sure to consider the endpoints). 

\medskip

\noindent c) Use your answer to a) to express
$\displaystyle\int_0^1{{2}\over{3x^4+16}}\,dx$ as the sum of an infinite
series.









\vfil\eject\end