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PI/4 = 1/1 - 1/3 + 1/5 - 1/7 + ...
Beat that
Lord Brouncker's Formula
4/PI = 1 + 1
----------------
2 + 32
------------
2 + 52
---------
2 + 72 ...
(PI2)/8 = 1/12 + 1/32 + 1/52 + ...
(PI2)/24 = 1/22 + 1/42 + 1/62 + ...
HAHA
Euler's Formula
(PI2)/6 = (n = 1..) 1/n2 = 1/12 + 1/22 + 1/32 + ...
(or more generally...)
(n = 1..) 1/n(2k) = (-1)(k-1) PI(2k) 2(2k) B(2k) / ( 2(2k)!)
B(k) = the k th Bernoulli number. eg. B0=1 B1=-1/2 B2=1/6 B4=-1/30 B6=1/42 B8=-1/30 B10=5/66. Further Bernoulli numbers are defined as (n 0)B0 + (n 1)B1 + (n 2)B2 + ... + (n (n-1))B(N-1) = 0 assuming all odd Bernoulli #'s > 1 are = 0. (n k) = binomial coefficient = n!/(k!(n-k)!)
On the other hand that bird flu is quite bad isn't it.
Bird flu can cause a range of symptoms in humans. Some patients report fever, cough, sore throat and muscle aches. Others suffer from eye infections, pneumonia, acute respiratory distress and other severe and life-threatening complications.