Suppose ak > 0 for all k, and ∑ ak converges.                                                   k=1 Answer the following questions and explain your reasoning.               ∞        a. Must ∑−3an always converge?               n=1               ∞ b. Must ∑ 1/an always converge?              n=1              ∞ c. Must ∑(an )^3 always

Q: #4 Short proofs and counterexamples, II. As before, determine if the statement is true or false. If…

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Q: xn = 1/n

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Q: (d) { cos(n n

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Q: sin vn 2n Determine the convergence of the sequence an . If it converges, find lim an. BIU A E EV…

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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: 1 3. En=1 (2n+1)3

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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: Determine convergence or divergence of TL A. converges B. diverges M 7n +6

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Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

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Q: Suppose that > an(x+9)" converges at a = 13. At which of the following values of x must the series…

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Q: (a) (b) (c) +8 {√n+1 = √n+ 2 } 2 ONG e n=1 In n +00 n=1 n=1

A: First put 5 terms and find value and look at the limit as n is large.

Q: 1. Determine whether the following converge or not (a) E k3 +1 k=1 2+1 (b) k=1

A: The given sequence is                                     ∑k=1∞k3k3+1  Consider     ak=k3k3+1 Now…

Q: the following converge or not

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Q: 3η 9.) Ž(-1 2η 9.) Σ n=1

A: Given: ∑n=1∞2nn-13n To Determine: Series is Convergent or Divergent Concept: Root Test:If we have…

Q: etermine if the following infinite product converges or II (1 e. Ïi (1+n 12) (-1)" n=1 00 II…

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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.