(3+3+3 points) In this problem, we will investigate the series k! k=0 (a) Show that lime-(1+-)* = e. Hint: try finding the limit of the natural logarithm instead. You will likely require L'Hopital's Rule. (b) Determine the radius of convergence r of this series. Note: r will be nonzero and finite. (c) Show that the series is divergent at the endpoints x = r and x = -r. Hint: Try finding an appropriate expansion of r* and compare it to k