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 n=1 √√√n² + 1 n² +5

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

A:

Q: 5. Which of the following series converge and w hich diverge? Explain your answers: Explain your…

A: (a) the given series is convergent. (b) the given series is divergent.

Q: 3" + 5" We would like to apply the Limit Comparison Test (Part 1) on the series 4" + 7" Which of the…

A: We have to find which series should we compare the given series to.

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: Use test of coarse divergence to show divergenceof the series.

A:

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

A:

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: 5. Does the series n=1 n+2n+1 converge? Explain. Upload Choose a File Question 6 6. Does the series…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

A:

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

A:

Q: 1 п-1 1 and А. В. D. ) C. n2 n3 n=1 n=1 n=1 n + 2 n2 1. Does this series converge or diverge? ? n=1…

A: First we will state limit comparison test then we will apply it on the given series

Q: 2. Which of the following series converge and which diverge? Explain your answers. (When checking an…

A:

Q: (-2)+1 1+3"

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

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…

Q: (x + 3)" (2n)! Consider the following power series: > Use the Ratio Test to determine the interval…

A:

Q: 1 En=1 n ln2 (n)

A:

Q: ∞ (b) Σne-ni n=3

A: To determine whether the series ∑n=3∞​ne−n2 converges or diverges, We'll use the Integral Test. The…