Lesson 3

Problem. Let \(P(n)\) be the number of ways to represent the number \(n\) as a sum of positive integers. Two representations are considered different even if they differ only in the order of the summands. For example, \(P(3)=4\): \[3=1+1+1, \quad 3=1+2, \quad 3=2+1, \quad 3=3 \ .\] What is \(P(6)\)?