Ramanujan's easiest formulaA while ago I decided to figure out how to prove one of Ramanujan’s formulas. I feel this is the sort of thing every mathematician should try at least once. I picked the easiest one I could find. Hardy called it one of the “least impressive". Still, it was pretty interesting: it turned out to be a puzzle within a puzzle! It has an easy outer layer which one can solve using standard ideas in calculus, and a tougher inner core which requires more cleverness.
You can see the slides here. For more, see these: