Ruby, 41 chars (using irb):
s=0;(3..3e6).step(4){|i|s+=8.0/i/(i-2)};s
Or this slightly longer, non-irb version:
s=0;(3..3e6).step(4){|i|s+=8.0/i/(i-2)};p s
This is a modified Leibniz:
- Combine pairs of terms. This gives you 2/3 + 2/35 + 2/99 + ...
- Pi becomes 8 * (1/(1 * 3) + 1/(5 * 7) + 1/(9 * 11) + ...)