It is not difficult to see that the numbers satisfy the inequalities p1 > p2...

It is not difficult to see that the numbers

satisfy the inequalities p1 > p2 > p3 > · · · > 0. Establish this fact. Next, use integration by parts to show that

and that p1 = 1. In the computer, use the recurrence relation to generate the first 20 values of p_n and explain why the inequalities shown are violated. Do not use subscripted variables. (See Dorn and McCracken [1972], pp. 120–129.)