\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Is every sequence the sequence of
partial sums for {\it some}\/ infinite series? If your answer to this
question is ``No'' give an example verifying that the assertion is
false. If your answer is ``Yes'' explain your reasoning, and, in
addition, find an infinite series whose sequence of partial sums is
$\left\{ {1 \over {n^2}} \right\}$. Does the series you have found
converge?









\vfil\eject\end