2. (3+3+3 points) In this problem, we will investigate the series K! k=0 (a) Show that lim. (1+2)

2. (3+3+3 points) In this problem, we will investigate the series f'kX (a) Show that lima (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 = r and r. Hint: Try finding k! an appropriate expansion of rk and compare it to nk.