(п+1 c) Σ-1 3η2 b) En=1(-1)" (41) Inn a) En=3 (in (Inn).

Q: Consider the series Σ(-1) 13. n3 " n=1 3" OA. The series diverges. B. The series is conditionally…

A: Solution

Q: Σ 2-2 (-1)" In n 1. Determine if the series is absolutely convergent. State which test you used, if…

A:

Q: 1. Determine if each series converges or diverges, you can use any of the tests discussed in class.…

A: a) ∑n=1∞3nen-1b) ∑n=1∞1+3n2nc) ∑n=3∞3n-14n

Q: 2n 82n+1 (c) 62 (Σ 72 n=5

A: The given series is c  ∑n=0∞ 2n82n+1d ∑n=0∞ 6n7n We have to determine whether the given series is a…

Q: (-3)'+i" (7n + 1) 4n25+ -2

A: Before starting solution steps , first I have written the Ratio test using that test I found that…

Q: Let an = 1+ ne¯n a) Does the sequence {an}n=0 converge or diverge? b) Does the series En=0 an…

A: Using ratio test:  limn→∞an+1an=limn→∞1+n+1e-n+11+ne-n                =limn→∞1n+1+1ne-n+11n+e-n…

Q: Use the Alternating Series Test to determine whether the alte S(-1)k+1_ k 7k + 8 00 k k = 1 Identify…

A:

Q: 3. If the following series is convergent, give its sum, showing all work. If it is divergent, write…

A: Given series is ∑n=1∞ 34n + 5n

Q: Question Which of the following statements applies to the convergent alternating series (−1)n+1 n+4…

A:

Q: Use the Ratio Test or Root Test to determine if each infinite series converges or diverges. 2" • a.…

A:

Q: 2" (2) ΣΠΩ (b) Σn, sin(n) n=0} {n-1 5+1 (c) Σ*1(−1)" /n n=1

A:

Q: 2n-3 00 Ση=1 5n+4

A: If limn→∞(∑n=0∞an)=L, where L= Number other than zero, then ∑n=0∞an divergesIf limn→∞(∑n=0∞an)=0,…

Q: Determine if the series converges or diverges. Give a reason for your answer. 5 - Σ n5"

A: Calculate as following:-

Q: 2 +.. 10000 converges? Justify your answers by recognizing this series as a geometric series. 2 2 3.…

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Q: Deermine whether the series is absolblel Convergent or condrlional Convergent 3 ナ n 1

A: The alternating series test is stated as below:

Q: Ση=1 (x + 1) η 3n? + η 2 1

A: Sol:- when x = -4 , then series becomes :- ∑n=1∞  -3n3nn2+1 =∑n=1∞ 3n-1n3nn2+1Cancel the common…

Q: 14. Determine which of the following series converge absolutely, converge conditionally or which…

A: