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You only need integration by parts to prove the irrationality of $\pi$. I'm having my Calculus 2 students do it as a long-term group project starting Monday.

Then when you've done partial fractions, you can have them derive the quickly-converging BBP formula for $\pi$.

And you can have them do the "18th Century Style" Euler argument for evaluating $\sum_{n=1}^\infty {1\over n^2}$.

Here's a link to two of these: http://homepages.wmich.edu/~jstrom/PiProjects/

1 [made Community Wiki]

You only need integration by parts to prove the irrationality of $\pi$. I'm having my Calculus 2 students do it as a long-term group project starting Monday.

Then when you've done partial fractions, you can have them derive the quickly-converging BBP formula for $\pi$.

And you can have them do the "18th Century Style" Euler argument for evaluating $\sum_{n=1}^\infty {1\over n^2}$.