ch of the following statements are correct for n2+1, n4+1 n² n=0 I) converges by the nth term test. II) converges by the limit comparison test with comparison n2 n=1

Q: Use the limit comparison test 5. 8n +7 In n- 2 n=1 O Converges O Diverges

A: We have to check whether given series is convergent or divergent.

Q: B) Prove that the sequence is convergent, where az = v2, = v2, 2+an, an+1 = %3D n 2

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Q: Consider the sequence P,3D0.3)4" the the order and the asymptotic error constant when the sequence…

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Q: k2 +k Use the limit comparison test to determine whether kA+2 converges.

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Q: Let (sn) be a sequence with lim sup sn = 10 and lim inf sn = 5. (a) Show that (sn) is bounded. (b)…

A: Consider a sequence, Sn, with lim sup Sn = 10 and lim inf Sn = 5. (a) To show that Sn is bounded. By…

Q: 3. Suppose an amount of money is invested at 8% per year. An additional amount of money equal to…

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Q: If we want to test convergence for to do the comparison ? 80 2n 2 n=1 n²+n+1 using the Limit…

A: (.)  Given series is,                  (.) Limit comparison test: Let  ,   be two positive term…

Q: n - 3 п - 3 1 (-1)" converges absolutely because 0 3. Зп + 1 Зп + 1 n=1

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Q: 7

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Q: What are all of the values of x ,such that (-1)*+(n) * converges? (). x1.40

A: Using ratio test a series converges iff:…

Q: True or false: if (n) converges, then every subsequence (n) is Cauchy. Select one: O True O False

A: True or false

Q: If we want to test convergence for n=1 2n-1 n³+n+1 using the Limit Comparison Test, what bn should…

A: This question is about sequence and series.

Q: / Find the limits of the following sequences and determine their convergence? an = n(1-cos — )

A: here I am using expension of function and then find the limits.

Q: For each of the following SEQUENCES, select whether they converge or diverge; for each that…

A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: 4. Use the basic comparison test (not the limit comparison test, or any other test) 00 Σ To show…

A: Given series : ∑n=0∞55n+5

Q: Just c and d

A: Please find the answer in next step

Q: converges? What are all of the values of x such that x1.20 >0.3 x<0.40

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Q: BySpsilon alefinition, checK the converrgence f sequences follustng the = nt 5n½

A: Here, let  Sn=3nn+5n12So,limn→∞Sn=limn→∞3nn+5n12             =limn→∞3nn1+5n…

Q: 9. Use the definition of convergence to prove that the sequence converges. b) {2n/(3n + 2)} c)…

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Q: Which step of the following of the proof of the fact that "if a -→ a, as n 0o, then JaJal" not true?…

A: For 1st the B option is correct .

Q: (-1)"+12na" n² + 3 V. Determine the interval of convergence of

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Q: Exercise 10.2.4. In view of Equation (10.2.2), one might suppose that the following is true: (Σ²).…

A: Given equality: ∑i=0nxi·∑i=0nyi=∑i=0nxiyi   a) Verify the equality is always true. If not, give an…

Q: 10a) Consider the following sequence of numbers defined recursively: a, = 3, a, = V3, az = V3 + v3.…

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Q: { h=1 (05/30) n+42

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Q: an 57" n! nal

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.