(2) Logarithmic p-series (a) Show that the improper integral | * ell (p a positive constant) Vv ) z(In x)P Pap converges if and only if p > 1. (b) What implications does the fact in part (a) have for the convergence of the series aaa *_, a, defined by the recursive formula of the terms 1+sin n converge or diverge? Give reasons for your answers. (5) Apply the Root Test in the series 2 du (5) a (a)radius and interval of convergence. to find its (b)For what values of x does the series converge. I. absolutely ? II. conditionally