Annoying Richard Taking Food

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A person named Richard Z is being extremely annoying. Each day, he takes some of Adam D's food. The amount of Adam's food is always the same. However, the good thing is that Adam is teaching Richard to stop taking food. In fact, every other day Richard even has a change of heart and gives back half the food he took the day prior. However, the next day, he takes back half of the food that he gave the day before.

Adam has 10 potatoes at the beginning, but loses some every day to Richard.

On his first day, Richard takes 4 potatoes. On his second, he gives 2. On his third, he takes 1, and on day four, he gives 1/2. This cycle of stealing and giving continues infinitely. How many potatoes will Adam end up with?

Express your answer to the nearest hundredth.


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