Comparison Test: Suppose that > an and) bn are series with positive terms. If n=1 n=1 an = C lim n-o bn where c is a finite number with c > 0, then either both series converge or both diverge. For the following problems, you must use the Limit Comparison Test. No points will be given for solutions that do not use the Limit Comparison Test. (a) Determine whether the series 5n 10 + 2n + 1 Vn4064 + 1 n=1 converges or diverges by comparing with 1 n2022 n=1 You have to use the Limit Comparison Test to justify your answer. (b) Determine whether the series Σ cot n=1 converges or diverges. You have to use the Limit Comparison Test to justify your answer. IM:

Q: 4. The series 10 5n² 3n²+1 (a) is Absolutely Convergent (b) is Conditionally Convergent, but not…

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Q: 1. Σ n=1 cos² (n) √n n5

A: Given series is                       Claim : To evaluate the convergence of series  .

Q: 5. For this problem, you have to read and study the textbook pages 762- 763 about The Limit…

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Q: 10. Determine whether the given series converges or diverges. If it converges, find its sum. -2 n=0…

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Q: 7. Determine whether the series Σn=1 n 5n 6n+2 is convergent or divergent.

A: Necessary condition for convergence  :                         Necessary condition for…

Q: The goal of this problem is to justify the following statement by using the Comparison Test for…

A: To prove the given statement using the comparison test.

Q: suppose San and Ση are series with positive terms and bn is known to be divergent. n (a) If an> bn…

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Q: Suppose that f(x) and g(x) are given by the power series and CO = By multiplying power series, find…

A: f(x)=5+5x+2x2+2x3+.......g(x)=4+2x+5x2+4x3h(x)=f(x).g(x)

Q: n³+2n²+3n-5 Does the series Σ=1 n6+3 converge or diverge? By what test?

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Q: Comparison Test: Suppose that an and b, are series with positive terms. n=1 n=1 If an lim = C n-00…

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Q: Consider the telescoping series (a) Find the partial sum Sn 2 Σ(11) +2 r+1 = + Σ(21) r + +1

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Q: 2. If am, bm, and Cm satisfy the inequalities 0 < am ≤ cm ≤ bm, for all m, what can we say about the…

A: Solution : Given that sequences

Q: 12. E-3 2n-5 Using the Direct Comparison Test show if the series is divergent of convergent

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Q: Evaluate the series > k=2 (-2)k+1 32k-1

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