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Question 7 Test the series below for convergence using the Ratio Test. (- 1)232n+1 n=0 (2n + 1)! Cn +1 The limit of the ratio test simplifies to lim where 1 -+ 00 Cn Cn+1 Cn The limit is: (enter oo for infinity if needed) Based on this, the serie: v Select an answer Diverges Submit Question ConvergesQuestion 8 Compute the value of the following improper integral, if it converges. (If it diverges, enter oo if it diverges to infinity, -oo if it diverges to negative infinity, or DNE if it diverges for some other reason. ) Hint: integrate by parts. 0 3 In(x) dx 00 3 In(n) What does the value of the improper integral tell use about the convergence of the series n =1 O the series converges O the series diverges O the Integral Test does not apply Submit QuestionQuestion 9 Compute the value of the improper integral. (If the integral diverges to co, type oo; if the integral diverges to - oo, type -oo; and if the integral diverges for some other reason, type DNE.) (2x + 7) 6 Use your answer to help determine whether the series E converges or diverges. Enter C if n =2 (2n+ 7) 6 the series is convergent, D if the series is divergent, or ? if the Integral Test does not apply: Submit