a n+1) %3D 2n Ans. Converges, 6)

Q: +00 e-l D) Jee - dz xe-1 1 a) converges to a negative value D to a positive value converges c)…

A: To check convergence of the following

Q: 2n? — п +9 Зп3 + 2n - 11 n=1

A: In this question we using Comparison test limn→∞unvn

Q: 4) If En=1 an converges, and if an # 1 and an> 0 for all n, a) Show that En-1 an converges. b) Does…

A: Comparison Test:Statement:If for all and converges, then also converges. If diverges, then also…

Q: Use the root test to determine whether >a, converges, where An is as follows. n=1 332. a, = n/ e"

A:

Q: The infinite sum Ea(n) A) S = a(n) has a finite limit B) none of these %3D converges if and only if

A: ∑n=1∞a(n) converges

Q: The sum of the series E-1 1-2n is: A) 1. B) 2. C) : D) 3

A: Here we have to find the sum of series ∑n=1∞121-2n

Q: The sum of the series E00 n%=D1 (5* – 5**) B) 3+ V5 C) 5+ v5 D) V5 E) 5

A: The expression, ∑n=1nak can be expanded as ∑n=1nak=a1+a2+a3+⋯+an .

Q: Question Cb). Diseuss condition for whieh faurier convergent. sexies is

A:

Q: ind the Laurent series of complex function f(z) = , for |z| < 3 %3D z-3 2 ) -(1 + ) + ) + ...) ) -(1…

A:

Q: Q.18) A series (-1)4+1 2k+1 , is: a) diverge by alternating series test c) converge by comparison…

A: I have appended the formula used in the solution part of the question

Q: 5. Complete the following two problems. a) Prove En=2 n(Inn)2 converges; b) Assume that lan…

A: To prove that the series  converges.Note: Since the student has posted multiple questions and does…

Q: cot(8)de is a) converges to - 1 b) converges to - 2 c) converges to -n d) diverges e) None of all

A:

Q: 3)the sequence a) Convergent converge 1. z, nln(l+-)+; = -t is n 2n-1 b) divergent c) absolutely…

A: The given sequence is zn=nln1+1n+n22n-1i.

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: Using the limit comparison test the appropriate bn that is used In(n) converges is: to make the…

A:

Q: Q8) The series 7 + 10cosn n4 n =1 a) converges by comparison test b) converges to 0

A: NOTE-By bartleby rules, only first two question has been answered. As per given by the question,…

Q: n + 3 2n + 1

A:

Q: Let an = 1+ ne¯n a) Does the sequence {an}=0 converge or diverge? ANS: CONVERGES b) Does the series…

A: It is given that the sequence an=1+ne-n. limn→∞an=limn→∞1+ne-n              =limn→∞1+nen…

Q: SELECT (n!)? (2n)! .()* B) is similar to G A) converges C) is similar to )" D) diverges

A: We will use Ratio Test to determine convergency

Q: Do these converge, (absolutely, Conditionally) or diverge ¹){( n=1 2.) 8 WE 2n+3 35n+1 3.). 8Wä 4.)…

A:

Q: Part C

A:

Q: (0) If lan diverges and (an Converges, n=1 (a) An Converges absolutely. n=D1 (b) Y An Converges…

A: We will get the conclusion by using the definition of a conditionally Convergent Series.  Option (b)…

Q: Q9) Compute J x-2)(x-3) d. 41 1. a) In- b)3In2 c) The integral diverges d) In2 5nl R10) The seies

A: Integration

Q: Q.2) Determine of each point convergens or diverges: (-1)"(3n)!/ /n! (n + 1)! (n+ 2)!

A: determine whether the series converges of diverges (i) ∑n=0∞-1n3n!n!n+1!n+2! we will use ratio test…

Q: (2n)! a"(n!)2 A) diverges if |a| 2² n-1 C) converges if |a| > 2ª

A: Here we have to find the converges or diverges of the given series.

Q: Find the sum of the series as a function of x. A) E(z +7)" B) n=1 I + 7 I+7 I + 8 I+ 6 D) I+7 I+7 I…

A:

Q: SntXn stx

A: We have to test the convergency.

Q: O (*+n)* Given fafx)= x*+n?' find NeN such that fu (x) converges to f(x) =1 Vx e [,-) a) E c) d)…

A:

Q: Σ Suppose that an = -1 and ) b, 9 and a1 = -8 and b, = - 6, find the sum of the n=1 n=1 series:…

A: