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\large\bf Project Based Math 112, Fall 2001\\
Sigma Detectives Revisited\\[.25in]
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Weeks ago you guessed the formula
$$\displaystyle\sum_{i=1}^n i^3 = \left[{n(n+1)\over 2}\right]^2.$$
Now it's time to prove it using mathematical induction.
To prove a formula by mathematical induction we need to show two
things:

\medskip
{\it Base Case}: The formula is true when $n=1$.

{\it Inductive Case}: If the formula happens to be true for $n$,
then it must also be true for $n+1$.
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{\bf(a)} Write out and prove the base case.

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{\bf(b)} Write out and prove the inductive case.

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{\sc Congratulations!}  You have done a proof by mathematical induction.

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