1.)

DHW 11 -- 11.2 - 11.3: Problem 1 (1 point) Determine whether the series is convergent or divergent. If convergent, find the sum. 4n n=1 Vn2 + 13 The series ? Justification: (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. This is a Geometric Series with r = and its sum is (Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, lim an = n->00 O C. This is a telescoping series with lim sn = n->00DHW 11 -- 11.2 - 11.3: Problem 2 (1 point) Determine whether the series is convergent or divergent. If convergent, find the sum. k(k + 11) K= 1 ( k + 10) 2 The series ? Justification converges r a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. This i diverges ries with r = and its sum is (Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, lim an = n->00 O C. This is a telescoping series with lim sn = n->00DHW 11 -- 11.2 - 11.3: Problem 3 (1 point) Determine whether the series is convergent or divergent. If convergent, find the sum. 1 1 - + ... 25 125 The series ? Justification: (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. This is a Geometric Series with r = and its sum is (Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, lim an = n->00 O C. This is a telescoping series with lim sn =DHW 11 -- 11.2 - 11.3: Problem 4 (1 point) Determine whether the series is convergent or divergent. If convergent, find the sum. 4 - 0.8 + 0.16 - 0.032 + . . . The series ? Justification: (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. This is a Geometric Series with r = and its sum is (Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, lim an = n->00 O C. This is a telescoping series with lim sn = n->00DHW 11 -- 11.2 - 11.3: Problem 5 (1 point) Determine whether the series is convergent or divergent. If convergent, find the sum. 3 (k - 1)2 The series ? Justification: (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. This is a Geometric Series with r = and its sum is . (Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, lim an = n->00 O C. This is a telescoping series with lim Sn = n->00DHW 11 -- 11.2 - 11.3: Problem 6 (1 point) Determine whether the series is convergent or divergent. If convergent, find the sum. _arctan 2n2 - 12 n=1 10n + 10 The series Justification: (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. This is a Geometric Series with r = and its sum is .(Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, lim an = n->00 O C. This is a telescoping series with lim sn = 1-+00DHW 11 -- 11.2 - 11.3: Problem 7 (1 point) Determine whether the series is convergent or divergent. If convergent, find the sum. _(-4 ) " 91-n n=1 The series ? Justification: (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. This is a Geometric Series with r = and its sum is (Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, lim an = O C. This is a telescoping series with lim sn = n->00DHW 11 -- 11.2 - 11.3: Problem 8 (1 point) Determine whether the series is convergent or divergent. If convergent, find the sum. In(2(n + 1)) - In(2n) n=1 The series ? Justification: (For limits, enter a number, "-infnity", "infinity", or "DNE" as appropriate.) O A. This is a Geometric Series with r = and its sum is (Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, lim an = n->00 O C. This is a telescoping series with lim Sn = n->00Determine whether the series is convergent or divergent. If convergent, find the sum. 00 5 Z n[ni2] r121 Theseries '? V. Justification: (For limits, enter a number, "-infnity , infinity", or "DNE" as appropriate.) O A. This is a Geometric Series with 1" = and its sum is . (Enter "DNE" if divergent.) O B. This is not a Geometric Series. By the Divergence Test, 1111] on = 11}00 O C. This is a telescoping series with lim 3,; = 71}00 Determine whether the series is convergent or divergent. If convergent, find the sum. :0: 3 + 10" 10" 11:1 The series ? v , and its sum is . (Enter "DNE" if divergent.) converges diverges Note: in 0rd this probiem all answers must be correct. Determine whether the series is convergent or divergent. If convergent, find the sum. ix 2n + 9n ) 11 ":1 12 The series ? v , and its sum is . (Enter "DNE" if divergent.) converges diverges Note: in 0rd this probiem ah' answers must be correct. Determine whether the series is convergent or divergent. If convergent, find the sum. 00 g . 23112 _ 3 _ 5n+1 :(3.. ) n=1 The series '? v , and its sum is . (Enter "DNE" if divergent.) Note: in 0rd converges this probiem all answers must be correct. diverges Suppose f(:c) is a positive, continuous, decreasing function for :c in the interval [1, 00), and {an} is the sequence defined by an 2 n) for every natural number n. a. If f(:17) do: converges, then Zen choose v because 1 "=1 W O DO {)0 A. gs) 03;; O [DO {)0 E f :1: do: