\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} a) Is there a power series whose
interval of convergence is the interval $(0,1]$, that is, the interval
defined by $0<x\le 1$?  Give an explicit series or explain why there
is no such series.

\medskip

\noindent b) Is there a power series whose interval of convergence is
the interval $(0,infty]$, that is, the interval defined by $0<x$?
Give an explicit series or explain why there is no such series.

\vfil\eject\end