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: 3. Determine which of the following series converge: (a) ( d) Σ 50 + 2n n= n=1 n O n (e) n=1 (2n2 –…

A: Please note that according to guidelines only first 3subparts is solved.

Q: Part 1. Test the convergence of the following power series. If convergent, solve for the interval,…

A: Test for the class convergence, using Ratio test.

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

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Q: V. Consider the power series +∞o Σ n=1 (x + 1)n 3√√n² + 1 1. Determine whether the resulting series…

A: Use Leibnitz test(given in next page) to show convergence at x=-4.For 2) use radius of convergence…

Q: 3. Determine whether the following series converges, and if so, find its sum. 1 ( a) Σ27l-n 4 (b) (n…

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: II. Find the value(s) of x (or the interval of convergence) 2. Σn=0 for each of the following power…

A: The power series is  ∑n=0∞ (-1)n+1(x-5)nn·5n

Q: Determine whether each of the following series is convergent or divergent using the appropriate test…

A: Note:- Here given series are varies from n equal 1 to infinity  If given series varies from 1 to n…

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: +oo 1 (2n)! ( a) Σ ( c) Σ-1)" 4n2 – 8n + 3 n=1 2" n=1 +00 In n (b) Σ-1)" n2 n=2

A:

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: Use the Comparison Test to determine if the series 5n – cos 2n n + n2 + 1 T=1 converges or diverges.

A: Comparison  Test :    If ∑n=1∞ an and ∑n=1∞ bn be the two positive term series and an≤ K.bn for all…

Q: 1. Use any method to determine whether the following series converges or dive (a) E(-1)" n=1 (-1)"+1…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: IV. Determine whether the given series is convergent or divergent. Justify your answers. +00 (2n)!…

A: The given series are, ∑n=1+∞116n2+8n-3       ∑n=1+∞-1n2n!2n+1        ∑n=1+∞-1nlnnn2

Q: 2 2. Consider the series Σx-₁(-). Find a formula for the nth partial sum S, and k k+2 determine if…

A: we have given series ∑k=1∞ 2k-2k+2

Q: 6. Determine if the following series converge. If so, determine the limit. (a) E(1-(-1)*+2) i=1 (»)…

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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: