Question about a power series
I was playing around with some power series stuff, and I wondered what I would get if I used cos(n) as the coefficient, and I was thinking it might not converge or it might be a pathological function or something .. I plugged it into excel and got some rough estimations, and it seemed to converge between 1 and 1, graphing a smooth curve
I ended up plugging the series into Mathematica and after some tweaking, I got
Sum(n:0 to inf) cos(n)x^n = (cos(1)x  1) / (x^2 + 2cos(1)x  1)
now .. how would you go about finding that out with pencil and paper?
