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{\large\bf Sums and Convergence}\\
{\large\bf Math 166}\\
\\ \hline
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{\Large
\begin{enumerate}

\item Use  Geometric series: ${\displaystyle \sum^\infty_{n=0}
2\left(-\frac{1}{2}\right)^n}$

\vspace*{.2in}

\item Use $n^{th}$ term Test: ${\displaystyle \sum^\infty_{n=1}
\frac{n}{2n+3}}$

\vspace*{.2in}

\item Use Integral Test: ${\displaystyle \sum^\infty_{n=1}
\frac{1}{2n+1}}$

\vspace*{.2in}

\item Use p-series: ${\displaystyle \sum^\infty_{n=1}
\frac{1}{n{\sqrt[3] n}}}$

\vspace*{.2in}

\item Use Comparison Test:  ${\displaystyle \sum^\infty_{n=1}
\frac{1}{\sqrt {n^3+1}}}$

\vspace*{.2in}

\item  Use Limit Comparison Test:  ${\displaystyle \sum^\infty_{n=1}
\frac{1}{2^n-5}}$

\vspace*{.2in}

\item Use Alternating Series Test:  ${\displaystyle \sum^\infty_{n=0}
\frac{(-1)^n}{(2n)!}}$

\vspace*{.2in}

\item Use Absolute Convergence Test: ${\displaystyle \sum^\infty_{n=1}
\frac{(-1)^{n+1}}{n\sqrt{n}}}$

\vspace*{.2in}

\item Use Ratio Test:  ${\displaystyle \sum^\infty_{n=1}
\frac{(-1)^{n+1}(n+2)}{n(n+1)}}$

\vspace*{.2in}

\item Use Root Test: ${\displaystyle \sum^\infty_{n=1}
\left(\frac{2n}{n+1}\right)^n}$

\end{enumerate}
}
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