convergent, or divergent. (Show reasonir (2n + 1)" (a) Σ (b) E (-1)" n/Inn 3"n! n=1 n=2

Q: 3n + 4 A) B) none of these 4 10n 3n +4 lim 4 10n #0 has NO HOPE of convergence since n00

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Q: 3-22 · Find the radius of convergence and interval of conver- gence of the series. (2x – 1)" 20.…

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Q: (-1)*. 5n' +n a. Absolutely Convergent b. Conditionally Convergent с. Divergent

A: We have to test

Q: 2n=1 4. Prove that the convergence of E=1 an where a, 2 0 implies the convergence of an 5. sin(2n-1…

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Q: n The value(s) of p for which the series Ln-11+n*)-p is convergent using the integral test: A) p2 1.…

A: Solution:-

Q: 100 (x– 6)" X- n = 0

A: Given

Q: 3n 00 En=1 n е — 2 e

A: Given series is ∑n=1∞3nen-2n

Q: COs n The series n3 n=1 (a) converges absolutely. (Б) converges conditionally. (c) diverges.

A:

Q: (-1)' n² + n n* + 2n+1 Absolutely Convergent a. b. Conditionally Convergent с. Divergent

A: Find the aboslute converges of the series using limit using series

Q: (-1)" + 1 a) Classify the series 2 n = 1 as either Absolutely Convergent or Conditionally…

A:

Q: 8n + 3 E(-1) "-1. n2+3 n=1 a) Determine whether or not the series is absolutely convergent. b)…

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Q: 8 (iv) [(-1) n=1 n :)" sin n n+1 [ Select] [Select] is conditionally convergent is divergent. is…

A:

Q: COS n 9. The series > n3 n=1 (a) converges absolutely. (b) converges conditionally. (c) diverges.

A: There are various tests to check the convergence of series. One of test is if a series converges…

Q: k+1 , -1)**(z–5)* k 3k Find the interval of convergence for the power series >E-1 Lk=1

A: using ratio test to find interval of convergence.

Q: nxn 5) Find all values of x for which Σn=1 (n+1)(2x+1)″ converges absolutely.

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Q: (-12)" Σ 100 n n= 3 n

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Q: (x+ 2)" n . Find the interval of convergence of the power series n3" n=0 (A) [–1,5) (B) [–1,5] (C)…

A: Solution:- ∑n=0∞x+2nn 3n un=x+2nn 3nun+1=x+2n+1n+1 3n+1 limn→∞ unun+1=limn→∞ x+2nn3nn1+1n3n+1x+2n+1

Q: (-1)" 2) The series n=1 is п a) Convergent, but not absolute b) Converges absolutely c) Diverges

A: Answer and explanation is given below...

Q: n! The series i (n+1)" is convergent.

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Q: Find the series convergent or diverges. If it is convergent find the limit. an = (2 + n3 ) / ( 1 +…

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Q: 7n-1 Consider the power series: > (п — 5)3 6" n=1 First apply the ratio test to find L and then use…

A:

Q: +00 1 Σ n=3 n · . Inn - +00 Σ m=1 3η5 + cos2 n – 1 4m? – 15 + π

A: The given problem is to determine the given series is convergent or divergent using convergence…

Q: (-1)* (k + 1) a* Σ 4k Find the interval of convergence for a) O(-0, 0) b) О (-4,4) с) О (-5, —3) d)…

A: Given : let

Q: 5"x" The radius of convergent for the series is : (n)(n+ 1) n=1 (a)co (b)0 (d) 5 (e) None

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Q: 2n+1 Test the convergence of E 2n=1 by limit comparison test. Vn3+1

A: we have to test the convergence by limit comprison test

Q: x3 + 3 27. The power series x + 2 +... converges if and only if n (A) -1 <x< 1 (D) -1 <x S 1 (B) -1…

A: Find the convergence of series

Q: (x- 4)" Σ 2n+2 What is the sum and n=1 convergent interval of the series? х— 2 (a) 0<x<4 16-4x х -4…

A:

Q: 2 (1 – 3x)² C1 C2 C3 = C4 Find the radius of convergence R = Represent the function CO || ∞ as a…

A: Solution:-

Q: 3"x" The radius of convergent for the series is : (n + 2)(n + 1) (a)o (b)0 (d) 3 (e) None O a O b O…

A:

Q: n2+1 The series n=1 2n3+1 8. E +5) is ans. convergent divergent nothing can be said oscillatory POCO…

A:

Q: -1 > The series Es is () Diverge (ii) Converge

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Q: 5(x-3)" 00 Σ find the interval of convergence For the power series: n² n=1

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Q: (x – 1)" Find all values of x for which the series converges. n3" n=1

A: We have to find the radius of convergence.

Q: (1) E (-1)*cn must converge if c, > 0 and lim Cn = 0. (ii) E ön must converge if 0 0 and lim 5. 0…

A:

Q: k-1 Determine whether or not the series of functions > x*- converges uniformly on [-a, a] k=1 with a…

A: Given series is the geometric series ∑k=1∞xk-1. To check the convergence of this series on -a,a…

Q: an k n=1 an k = 00 n=1 5n² +5n+ 5 5n5 + 6n +3 an ? 5n² + 5n+ 2 5n5 +6n + 3√√n, an ? Option:…

A:

Q: Using Sandwich Theorem 3n2 + 1 an = (-1)" n3 – 4 O converges to 1 O diverges O converges to -1 O…

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Q: CHE Example H·W : POI Test the convergence or divergence of the series by Root Test k k (3k+2)…

A: Root testIf limn→∞|an|1n=L, and:  If L&lt;1, then ∑an converges  If L&gt;1, then ∑an diverges  If…

Q: 00 (-1)*x* is: The interval of convergent for the series 4kk (a)[-4, 4] (b)(-4, 4] (c) [-4, 4)…

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Q: Using Sandwich Theorem 3n2 + 1 an = (-1)" n3 – 4 | O diverges O converges to 1 O converges to -1…

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Q: Question 3 (- whether it is convergent or divergent (show all ) Test the following series your…

A:

Q: Theorem 19 (Cauchy's Convergence) A series E-1 Xn converges if and only if Ve > 0, 3N eN such that…

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Q: 00 (-1)"n Does the series converge absolutely, converge conditionally, or diverge? n= 1

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Q: Using Sandwich Theorem 3n2 + 1 an = (-1)" n³ – 4 converges to 0 O converges to -1 O none of them O…

A: We have to find the limit by using sandwich theorem,…

Q: (-1)* 3E converges absolutely, converges Determine whether the series Σ conditionally, or diverges.…

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Q: 8 [(-1) ( √/2 + 1/2 ) n=1 The series A. diverges. B. converges to +∞. C. converges absolutely. D.…

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Q: n-1 The series E n=+00 is n=5 (i) Diverge (ii) Converge

A: Given : ∑n=5n=+∞eπn-1

Q: infinity sigma k=0  (-1)^k(k+1)x^k. Use that result to create a power series representation of f(x)…

A: To find the power series of the function:

Q: series onvergent, 8· 16 · 24 · (8n) .... n! n = 1 O absolutely convergent O conditionally convergent…

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Q: n(x-3)" Find the series' radius and interval of convergence Zn=1 2n /n2+1 100 Paragraph B IU A Lato…

A: