5. Determine if the following series converge conditionally, converge absolutely, or diverge. Justify your steps and cite the appropriate theorems and convergence/divergence tests. • (−1)"√n³ — 1 4n-1 n=1 b)Σ(³t+n)" 5n n=1 c) Σ cos (1) (-1)-1 5n²-4n+3 •[= Σ 4" 3n+7″

Q: Find all real numbers k so that the series (n – 3)* + (n – 3) (n³ – n³ – 1)'/3 n=4 converges.

A: Explanation of the answer is as follows

Q: 9. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

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Q: 00 b) Σ n=0 n?3* In(n + 2) 22n+2

A:

Q: #8: If the sum s of the series 3(-1)" (n+2) n=0 is approximated by 3(-1)" Sm (n+2) find the smallest…

A: The smallest possible m will be , m = 2.

Q: 8. Determine if the series diverges, or converges absolutely or conditionally. (-1)* 00 a) Ž /k (k –…

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Q: 2. Show whether the following alternating series converges absolutely, converges conditionally,…

A: Alternate series: When the series terms of a series  can be written in the form or , where , then,…

Q: n x + 2 .? х — 1 5. What is the domain of convergence of infinite series 3n n=1 What is the value of…

A: we have to find the domain of convergence of the given series and also find the value of it at X=-1

Q: 6. Use any test to determine whether each of the series below converge. State which test you are…

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Q: ) Investigate whether or not the following series converge. Justify your answer a. b. C. 8 k=1 00…

A: