consider the two sums SELECT ALL APPLICA A) A = In 2 A-Σα-1- B) series A and series B contain the same terms being added and C) b, = 3 + an - (-1)*** %3D 4n-1 D) a, = -- Σ-1+3 - F) Series B is absolutely Convergent B= E) +.. 8n-3 A = B G) b, = 2n(dn-1)(4n-3) H) Series A is absolutely Convergent I) using Limit Comparison Test b, ~ 14 15 17 1/4 15 13 1/2 12

Q: Find the Taylor series for f centered at 7 if (-1)^n! 3n (n + 1) f(n) (7) = n = 0 What is the radius…

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Q: For which p does the series 2 2" 13" converge? n = 1 Converges for p (In 2)/(In 3) Converges for p…

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Q: 9) Σ=1 10) 3/3 - (-1)^(1+n²) n! 3 1 4 2 11) Σ.» (= − 1) =0 τη 13) Σ=1 14) En=1 15) En=1 Σ + n+1 12)…

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Q: 3" +4" converges and find the limit of the series. 5" Prove the series n=1

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Q: 6) Which of the following series converges? 2n²+n+1 n²+1 a) En-o b) Emo (4)" (-)" d) None of the…

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Q: 2) Determine the sum it & converges of the infinite series if 26) 2/7 (-1²-13-2)

A: To determine the sum of the infinite series  if it converges. Concept used:The partial fraction…

Q: compute the series  i)  NΣn=1 1/(n2+2n).  ii)   ∞Σn=1 1/(n2+2n)

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Q: 12' >(- 1)"-'b. where b = n' 1=1 (n+2) 14"+3 a) Find and simplify bn+1 "q b) Test the given series…

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Q: 1 A sequence (m) is said to be contracture if there exists a constant k with ockal such that…

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Q: Which of the following sequences is a convergent and decreasing sequence with least upper bound 1?…

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Q: Find the interval of convergence of the power series: E (x- 3)"-1 (-1)" 72 a) (-1, 1] b) [2, 4] c)…

A: Use ratio test for checking the convergence

Q: Let {cn} be a positive, increasing sequence such that lim cn = 2. Determine whether the following…

A: Given that                                             limn→∞cn=2

Q: ) Find the interval of conver gence of the power Series * (4)" (n-2)_ (x -2)^ | n 2" n=3

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Q: • Σ(-1) -1. n=1 1 4η + 1

A: We have applied lebnitz test to find convergence of series

Q: Find the interval of convergence of the power series

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Q: +00 Suppose that E a, has positive terms and its partial sums s, n=1 +00 an satisfy the inequality…

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Q: Determine the radius of convergence of the power series (-1)"n2(x + 1)" 2" n=0

A: The given power series is ∑n=0∞-1nn2x+1n2n. Find the radius of converges for the power series.

Q: Find a closed form for the generating function for the sequence{an}, wherea) an = 5 for all n = 0,…

A: Hey, since there are multiple questions posted, we will answer first three sub parts. If you want…

Q: Зп + 1, A) 2n 4 — 2п n=1 n1-3n В) 42n n=0 (-5)1+2n C) 25п-3 n=4

A: Here we apply different tests like comparison test and Leibniz test.

Q: 2n+1 (2n-3 a.) = {(2²1 =3) "" } 116) (6.) = ( ³ + 05/(1+x)} 2n+5 11a) {a}={ O {c} = √√nº +3² +1 2n²…

A: Given: 11 a) an=2n-32n+52n+1, b) bn=3+cos3n+πn and c) cn=n6+3n2+12n2+3 To determine: Whether the…

Q: 3- (4z-5)" 5"

A: Given: ∑n=0∞4x-5n5n

Q: 11) E1 COs ()

A: As per bartleby guidelines we only give first question answers.

Q: If the sequence of the partial sums of a series a_n is {(5n − 1)/(3n + 7)}, then lim n→∞ a_n = 0. Is…

A: Explanation of the solution is given below..

Q: say if the series converge absolutely and explain through appropriate convergence test. If a…

A: Solution: Given that i ∑n=1∞-1n14n+7 Check absolute convergence first: an=∑n=1∞14n+7 let bn=1n , we…

Q: say if the series converge absolutely and explain through appropriate convergence test. If a…

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Q: By shifting the summation index of the following added three series n(n-1)C,r* + n(n – 1)C,x*-² -…

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Q: Which of the following sequences is a convergent and decreasing sequence with least upper bound 1?…

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Q: Q1) Find the Taylor series expansion in powers of x for f(x) = xln( xln(+²).

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.