I am having a bit of difficulty with the representation of functions as power series. I thought I understand the basic concept and was able to do the first 15 or so problems in Single Variable Calculus by James Stewart (3rd ed). However, the following is one of my homework questions.
Let fn = ((sin nx) / n2). Show that the series Σ fn(x) converges for all values of x but the series of derivatives Σ f ‘n (x) diverges when x = 2n Π (PI), n is an integer. For what values of x does the series Σ f “n (x) converge?
I asked the only other student in the class I know and he couldn't do it either. So any help would be greatly appreciated.