A nice round number

If you write dates with the month before the day, today is 3/14, or more affectionately, π day. Those who are especially meticulous celebrate at a moment about half a minute past 1:59. Yesterday, the Independent ran an article celebrating the wonderful properties and history of this number. Unfortunately, the following sentence appeared near the end of the story:

Pi, you see, is always going to be represented by an approximation because, like all irrational numbers, its digits never really end.

This is perfectly acceptable for a pre-calculus audience, but anyone who has been exposed to infinite sums deserves to see some of the miraculous closed-form expressions for π, such as the following, famously due to Ramanujan.

Happy π day!