Define the function g on R according to the following properties, where we use that Z+ 1/2 = {k +1/2 : keZ}. (i) g(x) = 0 for r EZ + 1/2. (ii) For all k E Z we put g(x) = x - k for r E (k - 1/2, k + 1/2). Next, define the function f on R by setting f(x) = g(nx) n2 n=1 (Click here for a visual representation of this function.)(b) Show that f is continuous on the set of points where all its partial sums are continuous. (c) Show that f is discontinuous at all other points. Hint: In (b), you need to combine two e-type definitions (continuity and convergence of an infinite series). Here, it is helpful if you can show that the N corresponding to a given E in the definition of the infinite series does not depend on x