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Old 12-08-2005, 10:07 AM
Posts: n/a
Default Re: Infinite multiplication

The log of the product is the sum of the logs, so one way to analyze this is to look at the series resulting from summing the logs of the numbers in your original sequence. If this sum diverges, then M=0. This happens if your numbers are all random with the same distribution, or you have the same repeated number. More generally, it will happen if the sequence of numbers that you are multiplying doesn't converge to 1, or converges slowly to 1. If the numbers in your sequence go to 1 quickly enough, then M can be non-zero.
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