\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Each of the following sequences has
limit $0$:
$$
\left\{{1\over{\sqrt n}}\right\}_{n=1}^\infty\qquad
\left\{{1\over{n}}\right\}_{n=1}^\infty\qquad
\left\{{1\over{n^2}}\right\}_{n=1}^\infty\qquad
\left\{{1\over{10^n}}\right\}_{n=1}^\infty
$$

\medskip

\noindent a) For each sequence, state exactly how large $n$ must be to
ensure that the term $a_n$ of the sequence (and all later terms as $n$
increases) satisfy $|a_n|<10^{-4}$.

\medskip

\noindent b) Similarly, how large must $n$ be to ensure that
$|a_n|<10^{-8}$? 

\medskip

\noindent c) Use this information to explain which sequence approaches
$0$ most rapidly and which approaches $0$ least rapidly.

\vfil\eject\end