1.)

Determine whether the series is absolutely convergent, conditionally convergent or divergent. (-1)n-1 4vn n=1 7n + 1 Part 1: Test _ lanl The series _ lanl ? ? Justification: converges diverges O A. By the Limit Companisun rest, let ) bn c where c = . P = , and n= 1 n=1 lim lanl n-too on O B. By the Divergence Test, lim |an| = n-+0o Part 2: Conclusion The series _ an is ? Justification: O A. _ lan| converges, therefore _ an is absolutely convergent by definition. O B. _ an converges by the Alternating Series Test, because: i) {bn } is ultimately decreasing because the function f satifying f(n) = bn is decreasing on the interval ii) lim bn = O C. _ an diverges byy the Divergence Test, because lim an = n-700Determine whether the series is absolutely convergent, conditionally convergent or divergent. f.(*1>\"(i%l n Part 1: Test 2 lal ._......;t..i, Justication: .I" A m w l U ' By the Limit Comparison Test, let 2 b\" : 2 6(7) where c : .p : ,and n:1 n:1 a lim|"'= ngnu b" O B. By the Divergence Test, [1131 lanl : n>m Part 2: Conclusion The series 2 an is ? v , Justication: O A. Z lanl converges, therefore 2 an is absolutely convergent by definition. Q B. :3 an converges by the Alternating Series Test. because: i) {bn} is ultimately decreasing because the function f satifying u) : b" is decreasing on the interval ii) 11m bu : O C. :3 an diverges byy the Divergence Test, because \"11331011\" : Determine whether the series is absolutely convergent, conditionally convergent or divergent. (-1)"(5n) n= 1 V25n4 - 3 Part 1: Test _ lanl The series E lanl ? ? Justification: converges diverges O A. By the Limit Comparison rest, let) where c = , P = , and n=1 n= 1 lim anl bn O B. By the Divergence Test, lim lan) = n-+00 Part 2: Conclusion The series _ an is ? Justification: O A. _ lanl converges, therefore _ an is absolutely convergent by definition. O B. _ an converges by the Alternating Series Test, because: i) {bn } is ultimately decreasing because the function f satifying f(n) = bn is decreasing on the interval ii) lim bn =Determine whether the series is absolutely convergent, conditionally convergent or divergent. C(-1)-1V8n' + 14 n=1 2n5 + 8 Part 1: Test _ lanl The series _ lanl ? Justification: O A. By the Limit Comparison Test, let ) bn = c np where c = , P = , and n=1 n=1 lim anl n too on O B. By the Divergence Test, lim lan| = Part 2: Conclusion The series _ an is ? ? Justification: absolutely convergent conditionally cnovergent O A. _ lan| conver divergent convergent by definition. O B. _ an converges by the Alternating Series Test, because: i) {bn } is ultimately decreasing because the function f satifying f(n) = bn is decreasing on the interval ii) lim bn = O C. _ an diverges byy the Divergence Test, because lim an =Determine whether the series is convergent or divergent. 8 n ! 7n The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim an+1 n-too an O B. By the Root Test, lim, +0. Vanl =Determine whether the series is convergent or divergent. no n=1 The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim anti 1-700 an O B. By the Root Test, lim, . Vanl =Determine whether the series is convergent or divergent. 18 An2 + 9n + 1 n=1 11n2 + 13n + 7 The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim an+1 an O B. By the Root Test, lim, +0. Vanl =Determine whether the series is convergent or divergent. no ( - 2) " (2n)! The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim anti n-too an O B. By the Root Test, lim, +0. Vanl =Determine whether the series is convergent or divergent. 2n n= 1 4n2 + 1 The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim anti n-too an O B. By the Root Test, lim, +0. Vanl =Determine whether the series is convergent or divergent. 5n+1 n=1 (n + 1)7 6n-1 The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim an+1 n-70o an O B. By the Root Test, lim, 0. Vanl =Determine whether the series is convergent or divergent. n9 4n 72n+4 n=1 The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim an+1 an O B. By the Root Test, lim, too Vanl =Determine whether the series is convergent or divergent. 7n + 1 2n n=1 2n + 1 The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim an+1 an O B. By the Root Test, lim, 0. Vanl =Determine whether the series is convergent or divergent. 00 n" n=1 n ! The series is ? Justification: (Enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. By the Ratio Test, lim an+1 n-too an O B. By the Root Test, lim, +0. Van| =