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lauched rocket, recovers and loses ...

Source: Spanish Mathematical Olympiad 1982 P3

December 23, 2022
algebra

Problem Statement

A rocket is launched and reaches 120120 m in height; in the fall he loses 6060 m, then it recovers 4040 m, loses 30 30 again, gains 2424, loses 2020, etc. If the process continues indefinitely, at what height does it tend to stabilize?