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APMOPS 2006 Question 21

APMOPS · APMOPS 2006

Question 21

There are 2006 oranges. The first group of people consumed $1/2$ of the oranges, the second group consumed $1/3$ of the remaining oranges, the third group consumed $1/4$ of the remaining oranges, and so on. The 2005th group consumed $1/2006$ of the remaining oranges. Find the number of oranges left.