3. Given the power series n=0 (n!) (2n)! an+1 (a) Simplify and find the limit, n . an (b) State the radius of convergence and the endpoints. (c) There is no easy way to test the endpoints by hand. Substitute a = 4 into the series and sum it up in Python to determine if it converges or not. (d) Even that doesn't work for x =-4, but the series is alternating, so we will numerically estimate the Alternating Series Test limit. Let n= [10, 100, 1000, 10000] and use list comprehension to evaluate la, at these values. Based on this answer and your answer to (e), state the interval of convergence of the series. (e) Using the power series, plot 8, 83, and so on the same axes. Use your interval of conver- gence as the domain.