Assignment:
Consider the series n = 1 to infinity 1/( 1 + n^2 x)
(a) For what values of x in R does the series converge absolutely?
(b) On what intervals of R does it converge uniformly?
(c) On what intervals of R does it fail to converge uniformly?
(d) Is the series bounded on R?
Provide complete and step by step solution for the question and show calculations and use formulas.