Sum of reciprocals
Source: China TST 2006
June 18, 2006
algebrareciprocal sumExtremal combinatoricsmaximization
Problem Statement
Given positive integer , find the biggest real number which satisfy the condition that if the sum of the reciprocals of a set of integers (They can be the same.) that are greater than is less than , then we can divide the set of numbers into no more than groups so that the sum of reciprocals of every group is less than .