In Exercises 35-40 use the root test to analyze whether the given series converges or diverges. If the root test is inconclu- sive, use a different test to analyze the series. 5k 5k 36. E k² 4k+1 35. k=1 k 1 37. E 38. E k³ +1 k=0 Ink k=2 1+ 4k k kk 39. E 40. 5k – 1, k=1 k! k=1

Q: From Rogawski ET 2e section 10.2, exercise 36. Use the formula for the sum of a geometric series to…

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Q: Determine if the series converges or diverges and select an appropriate test. (Only select one test…

A: →Comparison test for convergenceLet ∑un and ∑vn are two series such that limn→∞|unvn|=l ≠0 (a finite…

Q: Determine whether the series converges or diverges. 4 1 + e-n n = 1 O converges O diverges

A: Consider the series  ∑n=1∞ 1+1n4e−n

Q: Use the alternating series test to determine if the series converges or diverges. E(- 1)n²+1 n3 n =1

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Q: Determine whether the series converges or diverges. n² Σ (n + 2)! n=1

A: Given that  ∑n=1∞n2n+2!

Q: Determine whether the alternating series £ (-1)n+1, n3 converges or diverges. n= 1

A: Given alternating series is  ∑n=1∞-1n+13nn3

Q: 4η-3 (3) Σ=c 2=0 2η5

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Q: 1-

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Q: Exercise 1. Determine if the series converges or diverges. E(-1)"n sin () n=1

A: Given series is

Q: Determine whether the series converges or diverges. 1 Σ 3n + 2 n = 1 converges diverges

A: We will solve the problem

Q: 6. Use the root test to determine whether the series converges or diverges: k 2k3+3 5k2 + 1 k=1

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Q: Exercise 2 . Determine if the series converges or diverges. tan-(n) n/n + 6 n=1

A: The solution are next step..

Q: Determine if the series converges or diverges and select an appropriate test. n2+3n+1 Σ n=1 n°+2n+5…

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Q: 9. Use the alternating series test to determine whether 2(-1)"ne-" converges or diverges. n=1

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Q: Determine whether the series converges or diverges. 7n² – 1 5 n = 5 6n° + 5 converges diverges

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Q: Write out the first five terms for the series: (-1)** 2n Does this series converge or diverge?…

A: Consider the given alternative series as ∑n=1∞-1n+12n. Answer: The given series is converge It is…

Q: By using Alternating series test,determine if the series converges or diverges: 00 k E(-1)*. k2 + 1…

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Q: 12. Use Ratio Test to determine whether the series converges or diverges. If the test is…

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Q: EXERCISE 7. Determine if the series converges or diverges. Briefly justify!

A: Series convergence test. Since you have posted a question with multiple sub-parts, we will solve…

Q: Determine whether the series converges or diverges. 2n - n3 n = 1 +n+ 3 converges diverges

A: Solution

Q: 3. Determine whether the series E-1(-1)" * -is conditionally convergent, n2+1 absolutely convergent,…

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Q: Determine if the series converges or diverges. 3n А. [ Select ] nn n=1

A: Note: Since we can solve at most 3 subparts in a question, we have solved the thirst three…

Q: Determine if the series converges or diverges. W

A: Given: ∑n=1∞(-1)n10n(n+1)!

Q: +0o In n E(-1)" n2 n=2

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Q: By using Alternating series test,determine if the series converges or diverges: (-1)k–1 VE k=1

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Q: 1 3n² + 2 n=1

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Q: Determine whether the given series converges absolutely, converges conditionally, or diverges. k² +…

A: To Determine: Whether the given series converges conditionally, absolutely, or diverges.…

Q: Determine whether the series converges absolutely, converges conditionally, ges. 4n Σ(-1)", n³+1 n=2

A: Use alternating series test for checking the convergence .

Q: Ln(k) Σ k = 2 1)k k

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Q: Determine whether the series converges or diverges. n2 - 2n n3 + 6n + 3 n = 1 converges diverges

A: Q1. Divergent Q2. Convergent

Q: Determine whether the series converges or diverges. 8 2 Σ (1 + ²)²³0² e n = 1 converges diverges -…

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Q: In Exercises 45–54, (a) find the series' radius and interval of conver- gence. Then identify the…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 5 Σ 3 n=1 n° +2n´ – 3n +1 8.

A: We have to test

Q: +oo (-1)"+1 n=1

A: To show the convergence using alternating series test.

Q: In Exercises 19–26, determine whether the series converges ab, lutely, converges conditionally, or…

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Q: In Exercises 25-42, determine whether the series converges or diverges. Find the sum for the…

A: By applying root test

Q: Determine whether the series converges or diverges. Σ 2n + 4 n = 1 O converges O diverges

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Q: (b) Determine whether the alternating series converges or diverges by using the alternating series…

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Q: 2n² n2n n=1

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Q: By using Alternating series test,determine if the series converges or diverges: (-1)k+1 k + 2

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Q: Determine whether the series converges or diverges. Σ e2/n n = 1 O converges O diverges

A: Given series is, ∑n=1∞e2/nn

Q: 6. Use the p-series test to determine whether the series converges or diverges.

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Q: In exercises 1-24, determine whether the series converges or diverges. For convergent series, find…

A: We have to determine whether the series is convergent or divergent if convergent then find the sum.…

Q: In Exercises 15-21, use the ratio test to decide whether the series converges or diverges. 15. 16. 2…

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Q: Determine whether the series converges or diverges. n = 1 O converges diverges

A: Given query is to find series converges or diverges.

Q: Exercise 3. Determine if the series converges or diverges. Σ (n!)4 (7n)! n=1

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Q: PART III Q5. Determine whether the following series converges absolutely, converges conditionally,…

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Q: 14. Use the Alternating Series Test to determine whether the series below converges or diverges.…

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Q: From Rogawski ET 2e section 10.2, exercise 25. Use the formula for the sum of a geometric series to…

A: Given series:∑n=4∞7n12n To find the sum of the given series. Formula used: Sum of infinite geometric…