Part II: Determine if the following series are convergent or divergent. You should use each of the integral test, the limit comparison test, and the comparison test exactly once. 1 1 (k!)2 (iii) k2 k=1 k2 – 2k k=1 (2k)! k=1 (Hint: The series E * may be useful.) k=1 2k IM:

Q: Both of the following series converge by comparison to En=12 3 3 and 24n² + 7 24n2 – 7 n=1 n=1…

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Q: 4n+3 Examine the convergence of the series En=o,AT by applying limit comparison test.

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Q: (-1)" +1 (3x)" What are all of the values of x , such that * converges? n=1 .1 1 3 .3 X>0 .4 x> 3

A: Applying Root test for the series, the problem is solved

Q: Using Nth term test, the following series 2n2 + 3ln (n) 3n2 + 5 is convergent. The test is…

A: Given ∑n=1∞2n2+3 ln(n)3n2+5 Nth term test says that if the nth term of the sequence does not tend to…

Q: * 8 1-U 1=M 3 n = 2 (7) e n n³+1 = 20 Convergent / Divergent ? Conu. / Div. ?

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Q: What are all of the values of x ,such that Σ (3x)" (-1)"+ 00 converges? n=1

A: To solve this question we shall use root test for series.

Q: 5. For this problem, you have to read and study the textbook pages 762- 763 about The Limit…

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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: +00 (x+7)" ITEMS: Consider the power series n=2 2" Vn2 – 1' 1. Use Limit Comparison Test to show…

A: As per the policy we are providing the solutions of first three subparts. Given :  The given series…

Q: Show that E-2 ((In n)ª/n²) converges for -o 1. n=2

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Q: For the included problem, I keep getting that the series converges, but the correct answer is that…

A: First simplify as shown below.

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: 2 n+n+1 3″(n+1) n=1² n, 2

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Q: To test this series for convergence n=1 n /n³ +7 You could use the Limit Comparison Test, comparing…

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Q: 00 4" converges or diverges. (9n)2 t) Use the ratio test to determine whether> n=6 d the ratio of…

A: We have to use Ratio Test first.

Q: The series Lk = 1 (-1)*+1 is 2k divergent absolutely convergent conditionally convergent none

A: First I have written a short note about Absolutely and Conditionally convergent series and find tha…

Q: Σ 8n2 (:)"] 1 1 16n + 6 - n=100 3.

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Q: 17. Divergent or convergent? If convergent, show the lim n3 + 2 an 2n3 + 1

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Q: Comparison Test: Suppose that an and b, are series with positive terms. n=1 n=1 If an lim = C n-00…

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Q: 4(-1) (n+2) is approximated by 4(-1) 3m = m0 find the smallest possible m such that the alternating…

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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: 10. For converging sequence (an), let f, (æ)= (ar+1-az )x*. k=1 Then, does function sequence…

A: We are given a sequence of functions,   We need to check whether it is uniformly convergent in…

Q: Which of the following series is conditionally convergent? (A) B n=1 Σ(-1)²+1 17+n √n n=1 sin(n) 7²…

A: Given that, (A) The series  ∑n=1∞sin(n)n2 ,  Since,   ∑n=1∞ sin(n)n2 ≤   ∑n=1∞ 1n2 which is a…

Q: If akxk converges for x = -8, then which of the k=0 following must be true? I. ax* converges for x =…

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