Happy Pi day everyone!!

03162019, 04:23 PM
Post: #19




RE: Happy Pi day everyone!!
Sum of reciprocals of integers (limit of course) from One to Infinity (not starring Deborah Kerr and Frank Sinatra) is Pi^2/6.
Probability that two random (will define below) integers are coprime is 6/Pi^2. How to uniformly choose an integer at random. 1. Choose a large (not necessarily specified) integer: X. 2. Choose an integer within 1 to X with probability 1/X (using come criterion). 3. If the density of integers satisfy that criterion has a limit as X goes to infinity, the will choose an integer with the proper density. Example: Choose even integer within 1x. Probability is either 1/2 or 2X/(2*X+1) which has a limit 1/2 so we can meaningfully say that half of all integers are even. 

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