Use either the ratio test or the root test to determine whether the series converge or diverge. k 3k + 1 (a) 2k – 5 k=1 5k (b) E (k!)(k!) k=1

Q: Determine whether the series converges or diverges.

A: Consider the series

Q: Use any method to determine whether the series converge. (a) k=1 12k The series 1 (b) 2 12* + 1 k=1…

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Q: Determine whether or not the series converges

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Q: Determine whether the series converges or diverges. ∞ ∑…

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Q: Determine if the series converge absolutely, converges, or diverge 5n2 + 9 E (-1)n n=1 |8n8 +6…

A: The given series is: ∑n=1∞(-1)n5n2+98n8+6 Let, an=(-1)n5n2+98n8+6|an|=5n2+98n8+6

Q: b) Use the Ratio Test to determine if the series converges diverges. or n5" (2n + 3)ln (n + 1) n=1

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Q: Determine whether the series converges. k2 +2 2 +7 k=1 O The series diverges. O The series…

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Q: Determine whether the series converges. 1 k=I V2k – 1 The series converges. The series diverges.

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Q: Determine whether the series converges. Σk³ e-k4 k=1 The series >

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Q: Use the ratio test to determine if series converges or diverges. Σ 3(n!)2 (2n)! n=1

A: Solution: The objective is to determine whether the given series is convergent or divergent

Q: Use any method to determine whether the series converge. (a) k=1 The series 1 (b) 9k + 1 The series

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

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Q: +o0 а. n п+2 n=1

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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. Σ Vk+ 3 k=1 The series converges. The series diverges.

A: Given: ∑k=1∞1k+3 Using integral test of convergence. Integral test of convergence: If fx is…

Q: Determine whether the series (-1)". converges or diverges. Vn3 +2 n=1

A: Apply Leibniz test for convergence

Q: Use the indicated test to determine if the series converges or diverges. Fully justify your answer.…

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Q: Use the Comparison Test to determine whether the series converges. ∞ Σ k=1 1 3 7k³ +7 The Comparison…

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Q: Use the Comparison Test to determine whether the series converges or diverges. 2n n=1 2n 5n3 + 6…

A: Explanation of the answer is as follows

Q: Does the series converge or diverge?

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Q: Using either Comparison Test or Integral Test, determine whether the series converge or diverge. [5-…

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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: Determine whether the series converges or diverges. 4n³ Σ n²-4 11=2

A: Given series is  ∑n=2∞4n3n4-4 ....(1)=4∑n=2∞n3n4-4 ....(2)

Q: n² +2 4. Use a comparison test to determine if the series converges or diverges. n=1

A: Follow the steps.

Q: 27. Use the Ratio Test to determine the convergence or divergence of the series. * (- 3)*6" n! n=0…

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Q: Use the Alternating Series Test to determine whether the series converges. 00 2 Σ (-1)k+1. k=1 k 4…

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Q: Determine whether the series converges. Σ 1 k=1 2k – 1 The series converges. The series diverges.

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Q: Use the Comparison Test to determine whether the series converges. Σ k=1 1 8 5k° +6

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Q: Determine if the series converges or diverges. If the series converges give its value. 10 Σ 00 n=4…

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Q: n2 +3 Σ Determine whether the series is convergent divergent. or 2n2 – 3n

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Q: n2(-3)2n 10" (п3 — 1) n=3

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Q: Ln(k) Σ k = 2 1)k k

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Q: Determine if the series converges or diverges. If the series converges, find its sum. 1 1 Σ /n +1 Vn…

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Q: n=1 b) Use the Ratio Test to determine if the series converges or diverges. n5" L(2n + 3)ln (n + 1)…

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Q: 18. Use the Ratio test to determine if the series converges or 2n+1 diverges En=1 n 3n-1

A: See the details solution in below

Q: Use the limit comparison test to determine whether the series converges or diverges. 6k2 – 4k + 6…

A: Solve by limit comparison test :- if a known series and unknown series ratio after applying limit…

Q: + 8 W n = 2 ³√(¹-2) 4n³ +5

A: The given series is, ∑n=2∞n4-234n3+5   The limit comparison test for series says that, suppose ∑nan…

Q: (– 1)* 1 Vk8 + 2 k=1

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Q: Vk +1- Vk VR? + k Does the series converge? If it does, find the sum.

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Q: Apply the ratio test to determine whether or not the series converges. (−1)n-13n 2 n² 8 n=1

A: Ratio test is used

Q: Use the ratio test to determine if the series converges or diverges. (2n)! Σ 3^(nl)2 n=1 O Converges…

A: Ratio Test for the series :   If  ∑n=1∞ an be positive term series and L=limn→∞ an+1an , then  (i)…

Q: n! Consider the series: (-1)". (1)(3)(5)...(2n–1) Use the ratio test for absolute to determine…

A: Solution Given ∑n=1∞(-1)nn!(1)(3)(5)......(2n-1) Use the ratio test for absolute to determine…

Q: Determine the series' radius of convergence and interval of c Š (-1)*-'(x-1)" (2n-1)2" 00 п-1 1) n=1

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

Q: 27. Use the Ratio Test to determine the convergence or divergence of the series. (-3)"6" n! n =0 a.…

A: Ans is given below

Q: Use the limit comparison test to determine whether the series converges. Σ 3k +4 k=1 The series

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Q: 8. Use the Direct Comparison Test to determine whether the series converges or diverges. a. b. n=1…

A: To use the direct comparison test to check the convergence of the given series. Direct Comparison…

Q: 5* k!k! 10. Use the Ratio Test to determine whether the series converges or - (3k)! diverges.

A: Question is solved.

Q: b) Use the Ratio Test to determine if the series converges or diverges. n5" Σε (2n + 3)In (n + 1)…

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Q: Determine whether the series converges. 1 A V5k – 1 k=1 O The series converges. O The series…

A: 1 ∑k=1+∞15k-13let f(x)=15x-13By integral…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.