Here's a formula for pi that I found:

Pi = SUM_{k=0 to infinity}16^{-k}[ 4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6) ]

I just don't understand where the "k" came from. Here's the original article: http://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml.

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