In [1] : 1 from sympy import * 2 from sympy . plotting import (plot, plot_parametric) In [5]: 1 n = symbols ('n' , integet = True) 2 x = symbols ('x' , real = True) 3 a = (10**n) / (n + 1)*(4**(2*n+1) ) 4 RatioTest = abs(a. subs (n, n+1)/a) 5 print('The Ratio Test is', RatioTest. simplify ()) The Ratio Test is 160*Abs((n + 1)/(n + 2)) In [7]: a = ((factorial(n) )**2) / (2*n**3 + 5) 2 RatioTest = abs (a. subs (n, n+1)/a) W print( 'The Ratio Test is', RatioTest. simplify()) The Ratio Test is Abs((n + 1)**2*(2*n**3 + 5) /(2*n**3 + 6*n**2 + 6*n + 7) ) In [8]: a = ((-1)**n) / (n* (n+1) ) WNE RatioTest = abs(a. subs (n, n+1)/a) print('The Ratio Test is', RatioTest. simplify() ) The Ratio Test is Abs(n/ (n + 2) ) In [ ]: 12. Apply the Ratio Test to determine if each of the following series converges or not (or state if the test is inconclusive). Show each part of the computation, and make sure to simplify your expression first! If the Ratio Test fails, use a different convergence test to determine whether the series converges or diverges 10# (a) M (n + 1)43+1 (n!)? (b) 2n3 + 5 IM& IM : i (c) (-1)" n(n + 1) (both absolutely and conditionally)