The repertoire method

The repertoire method is an approach to find a closed-form for recurrence relations and sum of series. The method is introduced in Chapter 1 of ConMath but most readers at the first time struggled with it. Through the book, especially in Chapter 1 and 2, the repertoire method demonstrates its ability to solve many sums and recurrences. However, I honestly admit that it is quite difficult to apply and do not fully understand how it works.