Final answer:
The question provided seems unclear, mixing elements of probability, finance, and narrative elements related to lotteries. The main concepts involved could be expected value and infinite series, but without a clearer question, an accurate response cannot be given.
Step-by-step explanation:
The student seems to be asking about a hypothetical lottery game where payments increase each month and then reset and begin again the following year. Although the question contains some details and stories related to lotteries and gambling, the main concept here is related to expected value and possibly to the sum of an infinite series if you consider the payouts over an indefinite number of years. However, the question does not clearly state what is being asked. It appears that there are some hypothetical and narrative elements mixed with elements of probability and finance, so without a clearer question, providing a factual and accurate response is challenging.