Question: how to calculate the nth digit of pi?
Answer: Pi = SUMk=0 to infinity 16-k [ 4/(8k+1) – 2/(8k+4) – 1/(8k+5) – 1/(8k+6) ]. The reason this pi formula is so interesting is because it can be used to calculate the N-th digit of Pi (in base 16) without having to calculate all of the previous digits!