(-1)" In n Zn=2 to Σn=1 → Converges by alternating series test. But does not converge absolutely by direct comparison So, the series converges conditionally. 1 n

Q: 1. Determine whether each of the following series converges absolutely, con- verges conditionally or…

A: answer is in next step  . as per guideline i can answer only 3 subpart .

Q: Use the root test to determine whether the series converges or diverges. n8 n= 5n+1 Since lim which…

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Q: 4n+3 Examine the convergence of the series En=o,AT by applying limit comparison test.

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Q: 8 The series (-1)" n=1 2 √n O divergent is conditionally divergent both absolutely and conditionally…

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Q: 1 1 = 5° 0² J exp(-x²) dx

A: Using trapezoid rule

Q: (-1)" d) Find the sum of the series En=0 n! using the Alternating Series Theorem correct to three…

A: To find the sum of the series we must know about the series of ex , putting x=-1 in the series of ex…

Q: Let E2(-1)"a,n a series that satisfies the hypotheses of the alternating series criterion. let s be…

A: Given Series ∑n=2∞(-1)nan   satisfies the hypothesis of the alternative series criterion. If…

Q: We want to use the Alternating Series Test to determine if the series: k² k6+ 18 Σ(-1)*+2 k=4…

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Q: F(x) = (-1)". n3n n=1

A: Given series ∑n=1∞(-1)nxnn3n

Q: Consider the series (k!)³ (3k)! k=0 Determine if the series converges or diverges.

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Q: Determine if the series is converg

A: (a) Given, the infinite series             ∑n=1∞1+cosnen

Q: 15 - Use alternating series test (Leibnitz test) to decide that which ones of the following…

A: Leibnitz test. First and second series are convergent.

Q: compute the series  ∞Σn=1 1/(n2+2n)

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Q: 1. ii) and ii): 4 Determine whether each series converges or diverges. Justify your answer for both…

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Q: Determine whether the series converges absolutely or conditionally, or diverges. 5 (-1)" + '(6n + 8)…

A: The solution are next step..

Q: 32. Show if the series converges or diverges using the Alternating Series test 00 1n+1 Vn n=1

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Q: 3. Test the convergence of the series an Convergo ¹00 2n=1 n*+2n²+1 no +3

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Q: Which of the following series converge absolutely, which converge conditionally, and which diverge?

A: Given  1. ∑n=2∞-1nnn3-52. ∑n=0∞-1nn2+1n2+n+83. ∑n=1∞-1n74-5nn

Q: (5) Find the interval of convergence of the power series (n!)? a". Show your work. (2n)! n=0 IM:

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Q: In (k²) ( - 1) k converge k + 9 k=2 absolutely, converge conditionally or diverge? Does the series…

A: Given: ∑k=2∞-1kln k2k+9 To find: Check the convergence. Alternate series test: If a series is given…

Q: 00 The series E is n=1 (i) Converge (ii) Diverge

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Q: 00 convergent series i is j=0

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Q: is The series (-2) ¹! nn n=1 Absolutely Convergent O Conditionally Convergent Divergent O Cannot Be…

A: According to guidelines i solve first question only. So kindly request you to repost the remaining…

Q: Consider the series E (In(2n + 1) – In(2n – 1)). n=1 (a) Let a, = In(2n + 1) – In(2n – 1). Does {a,}…

A: Given ∑n=1∞(ln(2n+1)-ln(2n-1))

Q: Determine convergence or divergence of C: 00 n(In(n10))²_100n O The series converges. The series…

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