Remember:
1 + 1/2 + 1/4 + 1/8 + .... = 2 (and not infinite!)
Exactly.. Was going to post something similar, but your explanation is spot in. The limit or final value approaches a number because you have diminishing returns on an exponential basis.. 0.01 + 0.001 + 0.0001 + 0.00001 to give you an extreme example. Once you get far out on the series, the incremental income, although non-zero, approaches zero at some point, and when it does, you make no more ROI, to any significant digit.
Agreed! But it also depends on what the geometric series is and at what rate it changes. While there is an upper bound as to how much can be made at a given instant, what we really want is the area under the curve because not only am I making money at this instant, but I've also made money in the past that needs to be added. Even if it is a geometric series, if the t for each n is one year, then I easily make a profit. It just depends on what that series is (how fast the decay actually is) and how long it stays at each stage.
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Area under the curve (integral) is relevant to continues quantities. Income (cash flows) are discrete sums.
Have a look at the current rate of increase of the difficulty, and tell me what do you expect as the average rate of increase of the difficulty. 1% a day? 2% a day? If you tell me that, I will be able to tell you how much money you can get from your investment.
The fact that you made already some money does not alter the fact that on the USB stick you will not make ROI. We are talking about ROI of the USB stick, not your business model in general.
For example, you can sell ice-cream and mine bitcoins, and make money on the former, while lose money on the later, and still have a profitable business. But the fact remains that you do not make ROI with the USB sticks, and you would be better off financially if you did not purchase the USB erupters, and did not mine.