1.

Is the series 5 (n+2)! 1000 absolutely convergent, conditionally convergent, or divergent? A student submits the following solution: Line 1: In this example an = (n+2): 1000* Line 2: To use the ratio test, we should evaluate the limit lim |94 +1 , and then interpret the result. (n+3) Line 3: lim = lim 10ogn+1 71+00 7 +00 (n + 2)! 100g Line 4: = lim [n+3)! 1000" 1-100 10003+1 (n + 2)! Line 5: = lim (n+2)1 . (n+3) . 1000* "-+0 1000" . 1000 . (n+2)! Line 6: = lim n+3 n->0 1000 Line 7: = 00 Line 8: Because the limit is oo, the ratio test tells us that the series ) (n+2)! 1000 - is divergent. a) Is the above solution correct? [ Select ] b) If it is incorrect, in which line is the first error? [ Select ] c) What is the correct final answer to the question? [ Select ]DO 371 Let's use the Ratio Test to find the convergence of the series E n=1 a) What is an in this example? [ Select ] V b) Evaluate the limit lim [ Select ] c) Your answer for (b) means that the series E 271 [ Select ] 1=1n Let's use the Root Test to find the convergence of the series _ (-1)"( n 3n+200 n=1 a) Evaluate the limit lim an [ Select ] v 20 b) Your answer for (a) means that the series (-1)2 n 3n+200 is: n=1 [ Select ] VWhich of the following statements are TRUE? Select all that apply. If lim =0.5 then the series ) an converges absolutely. 12-100 1=1 If lim = 1 then the series ) an converges conditionally. 12 100 O) The ratio test provides a way of measuring how fast the terms of a series approach 0. If lim #/|an | = 0 then the series _ an | is convergent. 1=1 If lim * an = oo then the series ) an diverges. 12-+Do n=1 The ratio test is often used to determine convergence of series involving factorials. If lim = 4 then the series ) an diverges. 1=1