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2014 KIMC keystage3-IWYMIC individual Question 13

xIMC · 2014 KIMC keystage3-IWYMIC individual

Question 13

On the blackboard are written the reciprocals of the first 2014 positive integers. In a move, we may erase two numbers and replace them by the sum of their sum and their product. Eventually, only one number remains. What is the maximum value of this number?