\problemdata
       {summation} % latex-friendly label for the prob.
        {summations, induction} % The topic(s) of the problem content.  
        {?} % Source (if known)                                          
        {S00 ps5-2} % Usage (list ones you are aware of). 
        {Jack Kwok, S02} % Last revision info (author, date).   

\begin{problem} 

Consider the following summation:
\[\sum_{k=2}^n {\frac{1}{k(k-1)}}\] 

\begin{problemparts}
\problempart
Find a closed form solution for this summation.

\hint Try using partial fractions to break $\frac{1}{k(k-1)}$
into a difference of two terms.

\problempart Use induction to verify your closed form solution (i.e.,
prove that it is correct).

\end{problemparts}


\end{problem}