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Old 12-08-2005, 10:09 PM
BruceZ BruceZ is offline
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Join Date: Sep 2002
Posts: 1,636
Default Re: Infinite multiplication

I wrote a perl script (before I saw your anwer), and it didn't seem to converge.

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This shows that it is converging. Convergence means that it gets closer and closer to some limit, even if it never actually gets there, and even if we can't identify the limit by any means other than by continuing the calculation to greater precision, as with the calculation of pi. Obviously if it converges to an irrational number, your calculations will never terminate. We know that this converges because the steps in the sum of logs are getting smaller slightly faster than the geometric series, which we know converges.
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