[seqfan] What is 2 * 2/3 * 4/3 * 4/5 * 6/5 * 6/7 * 8/7 * 8/9 * ... ?

Alonso Del Arte alonso.delarte at gmail.com
Sun Jun 24 19:36:14 CEST 2012

Product n = 1 to Infinity (n/(n + 1))^((-1)^n) is approximately 1.57079,
but it takes a lot of computation to get just those few digits. Searching
in the OEIS gives the decimal expansion of pi/2
as the top result, and I am of course inclined to believe that pi is
involved in this somehow, but I am not as strong with the calculus as I
would like to be. Getting a False from Mathematica on x == Pi/2 does not
completely convince me, however.

So I'm hoping for some insight from one of y'all on this infinite product.


Alonso del Arte
Author at SmashWords.com<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>

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