A rain reservoir has a capacity of 2 gallons, and initially contains 1.5 gallons. A farmer does not want the reservoir to empty completely, so  every day he only uses half of what is left. It rains almost every day,  and an additional 1 gallon flows into the tank. Prove by induction that  the total water in the tank is always under 2 gallons.

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To prove by mathematical induction that the total water in the tank is always under 2 gallons we can ... View the full answer