1)thee sin(-)dz by using the residues is equal to Z a) 2/7 b) 0 c) i2n d) 2) the series (-1)-¹ is (2n-1)! nai a) Convergent b) divergent c) absolutely converge converge d) conditionally

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: Consider the series ∞ (2x)n Σ n=1 n2 A) | Compute the limit: lim an+1 nx an Show your steps. B) |…

A: Step 1:​n=1∑∞​n2(2x)n​​Step 2:​Using the Ratio TestFor the Ratio Test, we consider the…

Q: 10 Prove whether the series converges or diverges. cos(nn) a) E 2n-1 b) Σ c) E '(n!)² (2n)!

A: By ratio test and Lebinitz test we can give the answer for both questions.

Q: which of the following SSeries Converge 7n 2n2+1, tan

A: Series and sequences

Q: 25. Choose the series that is convergent: ΑΣ A) 1+ n n+1 B ) Σ- 2 n n 4n n1 ο Σ7m 3 n n 2 D Σν+1 +4n…

A: In order to identify the convergence of series from given options, apply the divergence tests as…

Q: 12) Given a power series E anx", if lim da+1= L where 0 < L < o, then the radius an n=0 1 of…

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: 3) Find the laurent series expansion for: 1 a) z² sin , 0 D c) 1-cost (Z-2₁)3 7

A: 3. a) Let f(z)=z2sin1z ,0&lt;z&lt;R.  We also know for  z≠0 , sin1z=1z-13!z3+15!z5-... [by…

Q: (-1)*1 n +1 5) For the series n=1 a) Show the series converges by the alternating series test. b)…

A:

Q: 58) Which of the following statements are true? a) The integral dx converges. b) The seriesE)"…

A: We are entitled to solve only one question at a time. As the specified one is not mentioned, So we…

Q: 42) The series ) 1 converges if and only if n2-a n=1 a) a > 1 b) a 1 d) -1 (-1)"-1 sin( n=1 a)…

A:

Q: 1)thee sind by using the residues is equal to 121-1 a) 2/7 b) 0 c) 127 d) z

A: As per our company guideline we are supposed to answer only one question kindly post remaining one…

Q: 4.) Determine Hthe given series converges or diverges C.) E n*rn +2 (3)"

A:

Q: Using Sandwich Theorem, the sequence 2 an = 4 – Cos n2 + 1 - O diverges O converges to 4 converges…

A:

Q: 2. Find the sum of the series if 0 < x < c < 1: a) En³x" n=0 x" b) E n=1 (n + 1)

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

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: 16) If E an converges, then cos(am) diverges. n=1 n=1 a) True b) False

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: Consider the power series 80 an (x – 6)" n=1 of variable x and with (a some sequence. If it is known…

A: In this series we have to find whether the series is convergent of divergent.

Q: a) Find the radius of convergence and the interval of convergence for the -(-1)^(x-3)" 2n+1 series

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

Q: Questions 5 – 7: Find the sum of each infinite series, or state that the series diverges. e 5) 529)…

A:

Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: 11.57 A researcher conducts an experiment to examine the relationship between the weight gain of…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Q2) The summation of ex series is x" a) En=0 n! b) Σ-01 5+n! xn+1 c) En=0 (п-1)! d)

A: Given:   Let fx=ex To find the Maclaurin series coefficients, we must evaluate          dndxnfxx=0…