. Find the region of convergence of the following series: (b) n=1 1 (d) n!rn (-1)n-1 (e) E n.3"(r – 5)" n=1 IM:

Q: Find the radius of convergence for the following series: (3z - 2)" n-1 3" (n + 3)i O R=-2 R= 1 R= 00…

A: Given: ∑n=1∞3x-2n3nn+312

Q: Which of the following function has the Macularin series (-1)"4"" B. 1- x² C. A. 1 E. F. D. 1+ 4.72…

A: We will use basic knowledge of summations and Maclaurin series expansions to solve this question.

Q: Find the interval and radius of convergence for the following power series: n(x– 2)" 5"

A: Consider the provided question, We have to find the interval and radius of convergence of the given…

Q: 2. Which of the following series diverge by the BDT? (Σ(-2) k=0 ê (c) Σ Σ(1+1)" Σ(6) 13 (e) none of…

A: We have to check which series is divergent by basic divergent series test.

Q: Which of the following series converge? 1 (1) E e n= 100 n 100 (II) (1) Σ 0.99999 n=1 n - 1.00001…

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Q: Which one of the following series is divergent? 1 (A) 1 5n +n+7 (B) n3 + Vn n=1 n=2 5 (C) 5h (D) 9n…

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Q: For what values of x does the series converge conditionally? (-1)^+1(x+6) n6" Σ n=1 n O A. x=-12, x…

A:

Q: which of the following series are not convergent? Select one: a. Lk-0 , sin(kt) O b. Ek-0 55t1 O c.…

A: As per the question, we need to find one series which is not convergent. Let us start from option…

Q: Which of the followings are divergent series? I. In2 +.. In7 In3 In4 In5 In6 II. E(-1)" n4+1 II.…

A: Option (e) is correct.

Q: +00 4+ cos² n 1. 3n – Vn n=1

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

Q: 1 ´ (3n+1) In (5n + 2)' (5n +2)'

A:

Q: Which of the following series diverge? I. cos (2n) n=1 II. 1 1+ - п n=1 1 n + n2 III. n= (A) II only…

A: Here we can use divergence test to check whether a series diverges or not. Divergence test states…

Q: Which of the following series converge? II. ΙΣ i=ing a © I, II., and III. I. only. III. only. I. and…

A:

Q: 2. Determine if the following series converge; if they do, find their sum. (1) E()" n=1 1 ( b) Σ n²…

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Q: Which of the following series converge absolutely? a. (-1)" Σ n3 n=1 n=1 00 C. (-1)" Σ Vn n=1 b.

A: To find the Absolute Convergence of the given series.

Q: ind the radius of convergence for the series (х — 3)" Σ (n + 1)4" n=1

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Q: Find the Maclaurin series for the given function. 2x 00 2"x" O A. 2 n! n= 1 (- 1)" 2^x" Ов. Σ n! n=…

A: Given function is fx=e2x. Maclaurin's series of a function fx is given by…

Q: 5. Find the radius of convergence of the series. E (2n)!(x-1)" n= 1 R= 0 a. b. R =–1 c. R = 1 d. R…

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Q: Which of the following series converge? 2" + n1 I. 4" + n² n=1 4" II. ) 5n +n Tn=D1 n! III. 3n…

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Q: 3. Determine whether the following series converges, and if so, find its sum. 1 n2 (n+ 1)(n + 2) (b)…

A: Series and sequences, convergent or Divergent.. using geometric series, telescoping series and p-…

Q: Determine whether the following series are convergent or divergent: b) E1 cos nn) /n² 4n

A:

Q: 6. Determine if the following series converge. If so, determine the limit. (a) E(1-(-1)*+2) i=1 (»)…

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Q: 72 (G) 3 n=1 1 (k) n(Inn)2 n=2 Inn Vn n=1

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Q: Find the sum, if it exists, of the given series: E (arctan(n?) – arctan(n + 1)*)) n=1 O 1 2 O -T T 4…

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Q: (c) Find the sum of each of the following series. Σ |x| < 1 (i) 2 n(n - 1)x", n = 2

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…