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\problemgrouptitle{Series}

\begin{problemblock}[2]{Evaluate the sums of the following series. (Any value that is not an index being summed over should be treated as a postive integer constant.)}

\item $\displaystyle\sum_{i=2}^5\frac{i+2}{i-1}$
\answer{$\displaystyle\frac{41}{4}$}

\item $\displaystyle\sum_{k=1}^4 6k$
\answer{60}

\item $\displaystyle\sum_{i=1}^n\frac{i^2+1}{n^3}$
\answer{$\displaystyle\frac{1}{n^3}\left(\frac{2n^3+3n^2+n}{6}+n\right)=\frac{2n^2+3n+7}{6n^2}$}

\item $\displaystyle\sum_{i=1}^ni(i-3)$
\answer{$\displaystyle\frac{2n^3+3n^2+n}{6}-\frac{3n^2+3n}{2}=\frac{n^3-3n^2-4n}{3}$}

\end{problemblock}

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