%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                  %
%  Procedure for Testing Series                    %
%                                                  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\problemgrouptitle{Procedure for Testing Series}

\begin{problemblock}[2]{Determine whether the infinite series is absolutely convergent, conditionally convergent, or divergent.}

\addtoanswerkey{\begin{multicols}{2}}
  
\item $\displaystyle \sum_{n=1}^{\infty}  \frac{5n^3+4n+2}{7n^3+2n^2+6}$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1}  \frac {n^2}{5n^3+6}$
\answer{
conditionally convergent
}

\item $\displaystyle \sum_{n=1}^{\infty}(-1)^{n-1}   \frac{n^n}{(n!)^n}$
\answer{
absolutely convergent
}

\item $\displaystyle \sum_{n=1}^{\infty}(-1)^{n-1} \frac{e^n  2^n}{n  3^n}$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \tan^{-1} n$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \tan \left( \frac{n\pi+5}{4n+7}\right)$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty}  \frac{2n^3+4}{3n^5+6}$
\answer{
convergent
}

\item $\displaystyle \sum_{n=1}^{\infty}   \frac{50}{\sqrt n+10}$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty}  \frac{\cos \left(\frac 1n \right)}{n^2}$
\answer{
absolutely convergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{2}{n(n+2)}$
\answer{
absolutely convergent
}

\item $\displaystyle \sum_{n=1}^{\infty}    \left [ \ln (2n+3)-\ln (n+2) \right]$
\answer{
divergent
}

\item $\displaystyle \sum_{n=1}^{\infty}    \left (\frac{4}{3^n}+\frac 3{4^n}\right)$
\answer{
absolutely convergent
}

\item $\displaystyle \sum_{n=1}^{\infty} \frac{\cos n\pi}{n}$
\answer{
conditionally convergent
}

\item $\displaystyle \sum_{n=1}^{\infty} (-1)^{n+1}  \frac{5n+7}{2n^3+25}$
\answer{
absolutely convergent
}

\addtoanswerkey{\end{multicols}}

\end{problemblock}

%%% Local Variables:
%%% mode: latex
%%% TeX-master: "../master"
%%% End:
