1.)

Determine whe her the series is convergent or divergent. 00 511 W 4 71 n' :1 ) 911 W 7 71:1 The series ? v Justication: (If more than one test is appropriate, pick the first applicable test in the list.) . m -C' A. . . . . , J This is a Geometric Series of the form E 117'" 1 where a : n=1 'r : ,and its sum is '0 B. This is a Telescoping Series, lim 3,, = nave O C. By the Divergence Test, "Igloo.\" : O D. By the Direct Comparison Test, an S b\" with Z 5\" = Z C(), c = and 'p = O E. By the Direct Comparison Test, an 2 b\" where Eb" : Z c(%) where c : and p : C' F. By the Limit Comparison Test, let 2b,, = Z C() where c = ,p = , and '5) G. By the Alternating series test, i) {17"} is ultimately decreasing because the function f satisfying n] = 1),, is decreasing on the interval ii) rm [In : nrm O H. By the Integral Test, i) The function f satisfying n) : an is positive, continuous, and ultimately decreasing on the interval loft) ffr) (in: 2 O I' By the Ratio Test, ljm n-oo an+1 an O J. By the Root Test. lit,HOG " Ianl = (Enter "DNE" if divergent.) Determine whether the series is convergent or divergent. 1 n 2 nvInn The series ? Justification: (If more than one test is appropriate, pick the first applicable test in the list.) JA. This is a Geometric Series of the form > ar"-1 where a = ,r = , and its sum is (Enter "DNE" if divergent.) n=1 O B. This is a Telescoping Series, lim Sn = O C. By the Divergence Test, lim an = O D. By the Direct Comparison Test, an c(. ) where c = and p = O F. By the Limit Comparison Test, let _ On = Ec( m ) where c = , P = , and lim - an n too bn O G. By the Alternating series test, i) {bn} is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval ii) lim br = n-too O H. By the Integral Test, i) The function f satisfying f(n) = an is positive, continuous, and ultimately decreasing on the interval ") , f(z) da = O l. By the Ratio Test, lim an+1 an O J. By the Root Test, lim, too Vanl =Determine whether the series is convergent or divergent. f: 6122 7 8n 7 10 7 Cm + 10 n71 The series '? v , Justication: (If more than one test is appropriate, pick the first applicable test in the list.) , Lao C' A. . . . . 7 . . J This is a Geometric Series of the form or\" 1 where a : ,r : , and its sum is 71:1 0 B. This is a Telescoping Series, lim 3,, = new 0 C. By the Divergence Test, "lilac" : O D. By the Direct Comparison Test, an S 31,1 with Z: bn : 2 C(72), C : and P : O E. By the Direct Comparison Test, on 2 bn where 26,, : Z c(#) where c : and p : O F. By the Limit Comparison Test, iet 2b,, = E C( ) where C = ,p = .and L n? O G. By the Alternating series test, i) {17"} is ultimately decreasing because the function f satisfying ffn] = b\" is decreasing on the interval ii) lim b" = naoo , t I . By the Integral Test, i) The function f satisfying n) = on is positive, continuous, and ultimately decreasing on the interval info x) :1: = f" a '4 l' By the Ratio Test, 11131 "+1 naoo an O J. By the Root Test. MinnowQ \" ini = (Enter \"DNE" if divergent.) Determine whether the series is convergent or divergent. (nutter: Z The series 7 v . Justication: (If more than one test is appropriate, pick the first applicable test in the list.) , cc) (' A. . . . . 7 . . J This is a Geometric Series of the form E or\" 1 where a : ,7' : , and its sum is n:1 O B. This is a Telescoping Series, lim an = nave O C. By the Divergence Test, "115E211\" : O D. By the Direct Comparison Test, on 1)\" with 2 bn : Z C(). C : and P : O E. By the Direct Comparison Test, an 2 b" where Eb\" : Z C(l where c : and p : O F. By the Limit Comparison Test. let 2b,, = Z C() where c = ,p = .and O G. By the Alternating series test, i) {bu} is ultimately decreasing because the function f satisfying n) : bn is decreasing on the interval ii) 11m bn : TlDCI , \\ I . By the Integral Test, i) The function f satisfying u) : an is positive, continuous, and ultimately decreasing on the interval ii) IN f(m) d1 : ,-, a 'J I' By the Ratio Test, lim "+1 naoo a,\" O J. By the Root Test. ljmnaw \" Ianl = (Enter \"DNE\" it divergent.) Determine whether the series is convergent or divergent. The series ? v , Justication: (It more than one test is appropriate, pick the first applicable test in the list.) GA 00 ' This is a Geometric Series of the form inn1 where a = 7" = , and its sum is n=1 C) B. This is a Telescoping Series, [1131 5,. : naoo O C. By the Divergence Test, lim (1,, : noo O D. By the Direct Comparison Test, an S 13,, with Z bu : Z C(), C = and p = O E. By the Direct Comparison Test, an 2 b\" where 26,, : Z c(#) where C : and p : O F. By the Limit Comparison Test, let 26,. : Z c( ) where c : ,p : ,and L n): O G. By the Alternating series test, i) {an} is ultimately decreasing because the function f satisfying u] = b" is decreasing on the interval ii) lim bn : \"+00 , \\ I . By the Integral Test, i) The function f satisfying n) : an is positive, continuous, and ultimately decreasing on the interval ii) [00 x) it : r" a '1 I' By the Ratio Test, 11111 "+1 11700 (1,, O J. By the Root Test. mnaw \" ianl = (Enter "DNE" if divergent.) Determine whether the series is convergent or divergent. 00 Z 8 + cos(n) \":1 inn/E The series ? v Justication: (If more than one test is appropriate, pick the first applicable test in the list.) 0 A OD ' This is a Geometric Series of the form urn1 where a : 7" : , and its sum is n=1 0 B. This is a Telescoping Series, lim 5,. : nm O C. By the Divergence Test, lim (1,, : "$00 0 D. By the Direct Comparison Test, on S I)\" with 2 bn : Z C(nfi). C : and P : '0 E. By the Direct Comparison Test, on 2 b" where 2b,, = Z C(i where C = and p = O F. By the Limit Comparison Test, let Eb" : Z c( ) where C : ,p : ,and L n)? O G. By the Alternating series test, i) {bu} is ultimately decreasing because the function f satisfying n] : b" is decreasing on the interval ii) lim 5,, : O H. By the Integral Test, i) The function f satisfying u) = a" is positive, continuous, and ultimately decreasing on the interval ii) [O x) d1: = a. 'J I' By the Ratio Test, ljm \"+1 name an O J. By the Root Test, litmus. " illnl : (Enter "DNE'I it divergent.) Determine whether the series is convergent or divergent. f: v8n3+8n+14 4n\"3 + 1072 n:1 The series ? v , Justication: (If more than one test is appropriate, pick the first applicable test in the list.) 0 A. . . . . m , . . This is a Geometric Series of the form 2 am\" 1 where a : ,r : , and its sum is 71:1 O B. This is a Telescoping Series, lim an : \"700 O C. By the Divergence Test, lim a,n = \"$00 0 D. By the Direct Comparison Test, an S b" with X b : Z C($), c : and p : O E. By the Direct Comparison Test, an 2 b\" where Eb\" : Z C() where c : and p : O F. By the Limit Comparison Test. let 2b,. = Z C(ip) where c = ,p = .and O G. By the Alternating series test, i) {bu} is ultimately decreasing because the function f satisfying f('n.) : b\" is decreasing on the interval ii) hm bu = 71.4?00 0 H. By the Integral Test, i) The function f satisfying n) : an is positive, continuous, and ultimately decreasing on the interval ii) flw f(.r) d1 : . . . G- O I' By the Ratio Test, hm "+1 noo 11,-, O J. By the Root Test, litmus " lanl : (Enter \"DNE\" if divergent.) Determine whether the series is convergent or divergent. 00 Z (in + e'\" 2 \":1 5n 1 The series ? v Justication: (If more than one test is appropriate, pick the first applicable test in the list.) . 00 f' A. . . . . 7 . J This is a Geometric Series of the form E 117'" 1 where a : ,r' : , and its sum is 11:1 0 B. This is a Telescoping Series, lim 3,, = have 0 C. By the Divergence Test, "IiEgon" : O D. By the Direct Comparison Test, an S b" with E: b\" = 2 C(72). c = and 'p = O E. By the Direct Comparison Test, on 2 by, where Eb\" : E C(%) where c : and p : O F. By the Limit Comparison Test, iet Eb\" : Z c(#) where c : ,p : , and O G. By the Alternating series test, i) {an} is ultimately decreasing because the function f satisfying n] = b\" is decreasing on the interval ii) lim L7,, = 714900 , \\ I . By the Integral Test, i) The function f satisfying n) : an is positive, continuous, and ultimately decreasing on the interval 00 ii) f m) d1 2 1 11n+1 7 O l' By the Ratio Test, hm noo an Q J. By the Root Test, ljJIlnm " lanl : (Enter "DNE" if divergent.) Determine whether the series is convergent or divergent. f: 20 tan'1(3n) ":1 4n + 1 The series '? v , Justication: (If more than one test is appropriate, pick the first applicable test in the list.) , 00 C' A. . . . . , . . J This is a Geometric Series of the form E 117'" 1 where a : ,7" : , and its sum is n=1 0 B. This is a Telescoping Series, [hit an : \"ADO O C. By the Divergence Test, lim an = noo O D. By the Direct Comparison Test, an S b\" with Z 5,, = Z C(). c = and 'p = O E. By the Direct Comparison Test, an 2 b\" where Eb" : Z c(%) where c : and p : O F. By the Limit Comparison Test. let 2b,, : Z c( ] where c : ,p : .and L :11? (3 G. By the Alternating series test, i) {fin} is ultimately decreasing because the function f satisfying n] = b" is decreasing on the interval ii) lim [an : nave , t I . By the Integral Test, i) The function f satisfying u) : an is positive, continuous, and ultimately decreasing on the interval ii) /1'm at) d1 : f" a 'J l' By the Ratio Test. ljm n+1 naoo an O J. By the Root Test, limnew \" lGnl : (Enter "DNE" if divergent.) Determine whether the series is convergent or divergent. w 1 1 Z 6:171 T 671+] n:1 The series 7 v , Justication: (If more than one lest is appropriate, pick the first applicable test in the list.) 00 C' A. . . . . _ . . J This is a Geometric Series otthe form E 117'" 1 where a : ,7" : , and its sum is n=1 '0 B. This is a Telescoping Series, lim 3,, = new 0 C. By the Divergence Test, \"113390.\" 2 O D. By the Direct Comparison Test, an S b\" with Z 5,, = 2 C(72), C = and p = O E. By the Direct Comparison Test, on 2 b\" where 21),, : Z C() where C : and p : C' F. By the Limit Comparison Test. let 2b,, = Z C() where C = ,p = ,and O G. By the Alternating series test, i) {bu} is ultimately decreasing because the function f satisfying u] : bn is decreasing on the interval ii) lim b" : I . By the Integral Test, i) The function f satisfying n) = on is positive, continuous, and ultimately decreasing on the interval ii)'/1mf(:s)dz : O I' By the Ratio Test. ljm noo lln+1 (1n O J. By the Root Test, lining\") \" Ianl 2 (Enter "DNE'I it divergent.) Determine whether the series is convergent or divergent. 1)"(8n) ()0 ( Z; 8112 73 The series ? V , Justication: (If more than one test is appropriate, pick the first applicable test in the list.) . 00 C' A. . . . . 7 . J This is a Geometric Series of the form E 117'" 1 where a : ,7" : , and its sum is n=1 0 B. This is a Telescoping Series, lim an = \"HUG O o. By the Divergence Test, lim an : nroQ O D. By the Direct Comparison Test, an S b\" with E b\" = Z C(nilp). c = and p = O E. By the Direct Comparison Test, an 2 b" where Eb" : Z C() where c : and p : O F. By the Limit Comparison Test. let Eb" : E C(%) where c : ,p : .and (3 G. By the Alternating series test, i) {bu} is ultimately decreasing because the function f satisfying n] = b\" is decreasing on the interval ii) hm L7,, = naoo O H. By the Integral Test, i) The function f satisfying n) : an is positive, continuous, and ultimately decreasing on the interval ii)f2wf(1) d: = A a. 'J I' By the Ratio Test, lim \"+1 naoo an O J. By the Root Test, mnaw " ianl : (Enter "DNE" if divergent.) Determine whether the series is convergent or divergent. The series ? v , Justication: (If more than one test is appropriate, pick the first applicable test in the list.) ,., so 'J A' This is a Geometric Series of the form a'r'VI where a 2 ,7" 2 , and its sum is 1121 O B. This is a Telescoping Series, lim 3,, 2 \"H00 0 C. By the Divergence Test, 11m (1,, 2 #1200 O D. By the Direct Comparison Test, an S b" with 2 bn 2 Z C(), c 2 and p 2 O E. By the Direct Comparison Test, on 2 by, where Z 6,, 2 E C(%) where c 2 and p 2 O F. By the Limit Comparison Test, let 2b,, 2 Z C() where c 2 ,p 2 , and . an. .132; :7 2 O G. By the Alternating series test, i) {an} is ultimately decreasing because the function f satisfying n] 2 b" is decreasing on the interval ii) lim b" = 712900 0 H. By the Integral Test, i) The function f satisfying n) 2 an is positive, continuous, and ultimately decreasing on the interval ii) [0 x) (in: = O I' By the Ratio Test, lim \"Aloe an-il (1n O J. By the Root Test, Eln7,00 \" Iani : (Enter "DNE" it divergent.) Determine whether the series is convergent or divergent. i): 771 W 4 2\" 2n W 4 71:1 The series ? v , Justication: (If more than one test is appropriate, pick the first applicable test in the list.) 0 A. . . . . oo T,_1 , . This is a Geometric Series of the form 2 0.7" where a = ,'r = , and its sum is n=1 C' B. This is a Telescoping Series, lim 3,, = \"ADO O C. By the Divergence Test, lim an = noo O D. By the Direct Comparison Test, an S b\" with Z b,1 : Z C(), c = and p = O E. By the Direct Comparison Test, an 2 1),, where Eb\" : Z C() where c : and p : O F. By the Limit Comparison Test, let 2b,, : Z c( ) where c : ,p : ,and '5) G. By the Alternating series test, i) {bu} is ultimately decreasing because the function f satisfying u] : 11,, is decreasing on the interval ii) hm b" : 71.4900 0 H. By the Integral Test, i) The function f satisfying n) : an is positive, continuous, and ultimately decreasing on the interval ii) flw r) d3: : O l' By the Ratio Test, ljm nroo an lln+1 O J. By the Root Test, lilting\