The cosine of the 6. 10.) M. n=1 n +2n

Q: If an converges and > 0 for all n , can anything be said about E–? An an

A: Given that, ∑ an  converges We known that, the series if  ∑n = 1∞ an  is convergent then limn→∞ an =…

Q: 1. Try to use the ratio test or the root test to determine if the following converge or diverge. If…

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Q: 1 1) Does E0 k=l (4)*+(÷)* converge or diverge? 'k=1

A: Apply here limit comparison test

Q: Find the radius of convergence for 00 E (sin? n)æ". n=1

A: It is given that,∑n=1∞sin2nxn We have to find the radius of convergence. Now,we have…

Q: Find whether the shown expression below diverges or converges Show your solution and how you came up…

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Q: For which values of p does %3D1 converge? (1+e9n)4p

A: Given series is ∑n=1∞en1+e9n4p Here, we have fn=en1+e9n4p We know that, for a series ∑n=1∞fn to…

Q: Find the sum, if it converges. 7i-1 ΣΤ 10 The sum is (Type an integer or a simplified fraction.)

A: Given,             ∑i=1∞ 7710i-1

Q: if tn=Br" determine if the following values of r would cauie the terms to converge as n gets uery…

A: The given terms converge for large values of n if r≤1 a) Given r = 0.75 <1 Hence convergent.   b)…

Q: hich values of xER, does the 2 (x-4)? converges abs

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Q: Using Sandwich Theorem, the sequence 1 cos? n + 1 an = 4 - n converges to 4 converges to 2 diverges…

A: Given

Q: If da = 00. Then 1211 Select one: a. converges but we don't know the sum of it. b. diverges. C. We…

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Q: If Ea, converges and a, > 0 for all n, can anything be said about 2(1/a,)? Give reasons for your…

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Q: an+1 → l as n → o, Find the radius of convergence. Suppose that an n 2n An( – 36)" n=D1

A: Suppose that an+1an→1 as n→∞. The given series is ∑n=1∞an-36nx2n. Calculate the radius of…

Q: Σ () n+1 \ 3n 4n n=1 converges diverges

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Q: Which of the follo wing information is correct for the sequence 3 7 1 dx dx 1 dx dx (a) The sequence…

A: Given a1 = 13∫13dxx= 13lnx13= 13ln(3)-ln(1)= ln(3)3a2 = 15∫15dxx= 15lnx15= 15ln(5)-ln(1)= ln(5)5a3 =…

Q: The sequence ɑn = 1 + converges to the limit A) e B) ve C) Ve D) e? E) F) e? /2

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Q: e? dz (1 – z)?

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Q: t Z an = 3+040+ 0 +O … Find $s, o Does the sesies converge ? H what is the sum ?

A: We have the given series is ∑n=1∞an=3+0+0+0+... Here the first term a1=3 The second term a2=0 and…

Q: cos2 Converges because Cos for r > 1, and J converges

A: Given that: The integral is ∫1∞ cos2xx2 dx .

Q: * /In(n), cos?n COS n2 n=| Identify if it converges or diverges

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Q: V2+cos (n2+1) Use the basic comparison test to determine whether E1 n=D1 converges or n+en diverges.

A: To check the Convergency of the given series. We apply here Simple comparison Test and Ratio Test of…

Q: PART III: Decide whether each of the following converges absolutely or con- ditionally. Justify your…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: find the value it converges to

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Q: For which values of p does E converge? n=1 (n°+7)*5 (Use symbolic notation and fractions where…

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Q: Use the ratio test to determine whether a_n converges,where a_n is given in the following problems.…

A: The solution are next step

Q: Ene-n? n=1 O converges O diverges

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Q: n2n n=1 (1+n)³n converges O diverges

A: It is given that ∑n=1∞ n2n1+n3n. Denote the general term of the series by un.  un=n2n1+n3n. Use…

Q: If tn= Br" determine if the following values of r would cause the terms to converge as n gers very…

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Q: S 3n? + 2n + 1 n2p-1 + 137 n=1

A: The given series is: ∑n=1∞3n2+2n+1n2p-1+137 Let, an=3n2+2n+1n2p-1+137, bn=n2n2p-1=1n2p-3; n≥1

Q: 1 Check the convergence of J: dx e xvIn x

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Q: Question 5 Consider 1 11 1 1 1 3 where signs occur in pairs. Does it converge? 1100 117

A: Dirichlet’s test Let Σ an be an infinite series such that its partial sums sn = a1 + a2 +⋯+ an  are…

Q: Determine whether the following serie is convergent or divergent. Explain steps. 1 n + n cos? n n=1

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Q: For which values of p does E n=1 (nº+4)*P converge? 7p (Use symbolic notation and fractions where…

A: Consider the provided summation series,

Q: 20 does the sevies s I converge For what values d 'p'

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Q: 00 For which values of p does E converge? (n° +7)" n=1 (Use symbolic notation and fractions where…

A: Given problem:-

Q: cos (%) 00 2, n=1 n' +4n

A: cosx=1-x22!+x33!-x44!+---    ∑n=1∞1np  converge if p≥2 Given  ∑n=1∞cosn2n2+4n

Q: For which values of p does E n-1 (1+em) converge? (Give your answer as an interval in the form…

A: We need to find the value of p such that the given series converges. The given series is…

Q: Part 4 Suppose > anconverges to 8 and > b, converges to 5. What does (3an - 2b,) converge n=1 n=1…

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Q: Sn/2", l1/2". if n is a prime number otherwise. Let an Does Ea, converge? Give reasons for your…

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Q: es the sequences converges or diverges ? (n sin") , (cos) ,(cos 3. 2

A: We will use Ratio test to test convergency

Q: For which values of p does n=1 converge? (1+e 9n)4p

A: For which values of p does ∑n=1∞en1+e9n4p converge?

Q: Find the radius of convergence for E (sin? n)æ". n=1 Preview

A: Given series

Q: 00 2 Σ п(n + 4) n=1 In(n) 5. 7n n=1 4.

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Q: n3" E(-1)"; 22n+1 n=1

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Q: Answer the question in the below image. For which values of p does 2n=171+eny4p converge?

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Q: Find the sum, if it converges. Σ6 i= 1 The sum is (Type an integer or a simplified fraction.)

A: In this question we have to find the sum if the series is converges.

Q: If £a, converges and Eb, diverges, can anything be said about their term-by-term sum E(a, + b„)?…

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Q: 30レて

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Q: {au, ) IL x y² dx dy Q4-A) Show that the sequence B) Evaluate : ah (sinn)}, +sinh( converges to (1).

A: Given

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.