10. Determine if 00 n=1 (1) (n + 1)3 converges.

Q: Which of the following statements best justifies In(n+ 1)

A: We are given the following series.               We know that ln(x) < x. So, ln(n+1)/n will…

Q: 1 10. Determine by the root test if Ln=1 converges or diverges. (In(n+1))“

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Q: Prove {52 + 11/n} n=1 to infinity converges to 52 using the definition of a convergent sequence.

A: Prove {52 + 11/n} n=1 to infinity converges to 52 using the definition of a convergent sequence.

Q: Rigorously show that (-1)"-1. n2 +1 is conditionally convergent. n=1

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Q: Show the following statement is true or not with proof. If {n} converges then {[sn]} converges.

A: We have to show the following statement is true or not with proof. If {sn} converges then {|sn|}…

Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

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Q: 43) Suppose that an > 0 for all n and that n=1 anbn necessarily converge? ∞ Σa an converges. Suppose…

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Q: Select the answer choices that make the following statements TRUE. (-1)" [ Select ] a. n=1 (-1)" b.…

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Q: n Determine whether the sequence Zn = (1+i)n answer (you may use any theorem or example proved in…

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Q: 2. Which of the following sequences converge to zero? n2 (a) n2 + 1 (b) 2" (c)

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Q: 00 For which a does > n(In n)a converge? n=2

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Q: 10. Give an example that Xn X but Xn does not converge to X in probability.

A: 10. Let Xn=-X, for n=1,2,3,... where X~N(0,1). Now, the CDF of Xn is FXn(xn)=PXn≤xn, for xn∈ℝ and…

Q: 5. Show that the following sequence Pa - n be before pn-p| ≤5 x 10-²? 1 2n converges linearly to p =…

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Q: Σ (-1)* converges. Vk Determine whether k=1

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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: 5. Use the definition of convergence to prove that the sequence (sn) diverges where Sn = √n.

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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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