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A scientist is studying the number of active cases of a sickness. On day 1, there...

A scientist is studying the number of active cases of a sickness. On day 1, there is only 1 case. On every subsequent day n, (n ≥ 2), exactly half of the cases from the previous day have recovered, but exactly n/2 new cases from the population arise. Prove that any day n, there are never more than n active cases of the sickness. (*Don’t worry about rounding - you may write n/2 in your solution and not worry about if it is a whole number)

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