Does each of the following series converge or diverge? Why? Show all your work and MUST include the name of the convergence test you are using. (Your best three answers will be counted toward your grade. The 4th will be for extra credit) Recall: Here is a list of convergence test we have learned so far: I: Test of Divergence (or Divergence Test) II Integral Test III Direct/Limit Comparison Test IV Alternating Series Test(AST) V Well-known series V(a) Geometric Series V(b) p-Series (c) n=1 n² + 5

Q: Explain why the direct comparison test can not be used to determine the convergence or 1 divergence…

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Q: We want to use the Basic Comparison Test (sometimes called the Direct Comparison Test or just the…

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Q: Let {X,}1 be i.i.d. uniform random variables in (0, 0), for some 0 >0. Denote by Mn = max=1,2,.,n…

A: Given, xii=1n is i.i.d  uniform random variable in [0,θ], θ>0And,Mn=maxi=1,2,..,nXiMaximum order…

Q: 1 n n=1

A: We have to check whether the given series  ∑n=1∞nn-12  converges or diverges, by comparison or limit…

Q: Test for convergence or divergence, using one of the tests listed below. 1 Σ n3 - 343 n = 8…

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Q: • Define L²-distance. Then state a form of the law of large numbers. • Define convergence in…

A: The L2-distance  calculates the distance of the vector coordinate from the origin of the vector…

Q: Test for convergence or divergence and identify the test used. Σ In(n) n = 2 converges by the Direct…

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Q: Use a convergence test of your choice to determine whether the following series converges. 80 Σ k=1…

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Q: Part II: Determine if the following series are convergent or divergent. You should use each of the…

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Q: k! (ii) ek k=1

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: (d) 2n² +1 n=1 3+872

A: The objective of this question is to determine whether the given series converges or diverges. We…