\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Use the comparison or limit comparison test to decide if the following
series converge.
$$
\sum_{n=1}^\infty {{4-\sin n}\over{n^2+1}}\,;\qquad
\sum_{n=1}^\infty {{4-\sin n}\over{2^n+1}}\,.
$$

\noindent For each series which converges, give an approximation of
its sum, together with an error estimate, as follows. First calculate
the sum $s_5$ of the first $5$ terms, Then estimate the ``tail''
$\sum\limits_{n=6}^\infty a_n$ by comparing it with an appropriate improper
integral or geometric series.









\vfil\eject\end