Suppose \(P_1 = 1,\, P_2 = 2\) and for \(n>2,\,P_n = P_1 + P_2 + ... + P_{n−1} + 1\). Find the values of \(P_1, P_2, ..., P_8\). Can you find a simpler recursive formula for \(P_n\)? Can you give an explicit formula?