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\begin{document}
	
	\mbox{}
	\title{Problem Set 14: Alternating Series}
	
	\maketitle	
	
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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	%\section{Introduction} \label{sec:intro}
	\noindent {\footnotesize Note: Most of the problems were taken from the textbook} \cite{jS15}.
		
	\begin{problem}
		Test the series for convergence or divergence.
		\begin{enumerate}[label=\alph*), topsep=8pt, itemsep=8pt, partopsep=1ex, parsep=1ex]
			
			\item $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{3 + 5n}$;
			
			\item $\sum_{n=1}^\infty \frac {(-1)^nn^2}{n^2 + n + 1}$;
			
			\item $\sum_{n=1}^\infty \frac {(-1)^nn}{e^n}$;
			
			\item $\sum_{n=1}^\infty (-1)^{n-1}\tan^{-1}(n)$;
			
			\item $\sum_{n=1}^\infty \frac {n \cos \pi n}{2^n}$;
			
			\item $\sum_{n=1}^\infty (-1)^n \cos(\pi/n)$;
			
			\item $\sum_{n=1}^\infty (-1)^n \sin(\pi/n)$;
			
			\item $\sum_{n=1}^\infty (-1)^n\frac{n^n}{n!}$;
			
			\item $\sum_{n=1}^\infty (-1)^n(\sqrt{n+1} - \sqrt{n})$.
		\end{enumerate}
	\end{problem}
	
	\vspace{15pt}
	
	\begin{problem}
		Approximate the sum of the series correct to four decimal places.
		\begin{enumerate}[label=\alph*), topsep=8pt, itemsep=8pt, partopsep=1ex, parsep=1ex]
			
			\item $\sum_{n=1}^\infty \frac{(-1)^n}{(2n)!}$;
			
			\item $\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n^6}$;
			
			\item $\sum_{n=1}^\infty \frac{(-1)^{n-1}}{n4^n}$.
			
		\end{enumerate}
	\end{problem}
	
	\vspace{20pt}
	
	\begin{thebibliography}{20}
		
		\bibitem{jS15} J.~Stewart: \emph{Single Variable Calculus} 8th Edition, Cengage Learning, Boston 2015.
		
	\end{thebibliography}
	
\end{document}