(2) Logarithmic p-series (a) Show that the improper integral [ dx (p a positive constant) . p a positive constan 2 (In x)? converges if and only if p > 1. (b) What implications does the fact in part (a) have for the convergence of the series CO 1 Ds n(In n)P : n=2 Give reasons for your answer. (3) Use the Limit Comparison Test ( Limit Comparison with }>~_, (3) ) to determine if the series = 1 2k (1+) (4) Does the series }-*, an defined by the recursive formula of the terms 1+sin n An41 = ni An a, = 1, converge or diverge? Give reasons for your answers. (5) Apply the Root Test in the series 2 d (5) = (a)radius and interval of convergence. to find its (b)For what values of x does the series converge. I. absolutely ? II. conditionally