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[2] [18 POINTS] Determine if the following converge or diverge. [a] ♡ (2+cosn)2"-5 [b] ¿ (3n)!...
6. ... / 6 points) Determine if the following sequences converge or diverge. If they converge, give the limit. (a) an = (-1)" n+1 n (b) an = n In(n)
3. (18 pts) Determine if the following sequences converge or diverge. For those that converge, determine the limit of the sequence. Make sure to fully justify your answer! arctan(n) (a) an= n In +3 (b) bn = (-1)" n² + 40 + 4)
(1) Determine whether the following series converge or diverge: (a) Σ=0 η2 n=1 (b) Σ=0 520 και (c) Σ=2 /n ln (η) 2n (4) Σ. sin(1) η2 (e) Σ1 (1) Σ=1 n2-3n+1 ln(η).
Does sigma (3n^2-n+1)/sqrt(n^7+2n^2+5) converge or diverge using limit comparison test.
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't forget to state the tests from class that you are using!). If any of the convergent ones can be evaluated by the techniques we have learned in class, you should give their value as well. An: + 3n" + 7n +2 In(In(n)) (1) V3n13 - 2n° +55 +n +3 An In(n) 8] (ii) ns16 Σ (3n)! (n!) 33" (iv)
Q3: determine wither the following series are converge or diverge In(n? +3) n!.inn a) Σ=1 n=2 (n+3) n (n+2)! (12 point) c) Σ=2 8 b) Σ=1 3+ (3)an d) Σ-1 In(n) 3 (m)2
Compare each series below to a p-series to determine whether they converge or diverge. Write your answer using the correct language and format. 2. 11 1 +1 n #18 18 3. 3n + 2 n2+4
2 Determine whether the following the following sequences converge or diverge. If it converges, find the limit. (a) an = cos () 2n (b) a = In 2n + 1 3 (a) Does Î- (-)" converge or diverge? If it converges, find its sum. n=1 (b) Show how > 41-13-" can be written in the form of a geometric series. Does it converge or diverge? If it converges, find its sum. n=1
Question # 5. (8 marks) Determine which of the following series converge and which diverge (don't forget to state the tests from class that you are using!). If any of the convergent ones can be evaluated by the techniques we have learned in class, you should give their value as well. 4 + 3n" + 7n +2 In(In(n)) (1) Σ 3n13 - 2n° +58 +n +3 4n In(n) (ii) 16
Q3: determine wither the following series are converge or diverge Γαο In(n? +3) n!.Inn a) in=1 (n+3) (12 point) c) Σ=2 =2 n (n+2)! 8 b) Σ=1 (3+ (4)»2η d) Σ= n=1 ln(m) 3 (n)2